What is the best way to begin a slow burn friendship to relationship? I'm no good at these types of things and was wondering what people liked reading so that its not terrible and/or unrealistic. I also realize that my idea of romance is a little a large bit strange.
I feel this question might be a bit opinion based but I will answer it the best I can and as objectively as I can. Truthfully it depends on what kind of dynamic you want the couple to have. I suggest reading into relationship dynamics and different ways people are in a relationship. This can very easily have a BDSMesque style of relationship in terms of personality and power play or it can be very vanilla. While the style of their relationship may not directly answer the question, it is still something that gives you an idea where to start. Clearly your MC male is probably not the most romantic man in the world due to his past and profession. So having him plan out a very romantic first date would be out of character.
Think about your characters, what they would do and not do romantically based on their personalities. Who is the aggressor? Does one play hard to get? Maybe you want it to spark because he saves her during a combat mission. It just depends on how you want the story to go and how you want their relationship to mature.
I was writing a similar story once. Building romance is not the easiest of things, so I feel you.
I'd say that you have to put yourself in their shoes. Think of the most interesting or probable way of making the relationship happen. Personality, background, social context and situational events all matter.
It also depends on how much their relationship "fits" inside your plot. Does the main story revolve around their relationship, or is it something that happens on the side? The first is more likely, since you mentioned they both are main characters, but still this point holds.
If it's important for the plot (both in terms of story and character developmetn), consider that you will have more "time" to show how their relationship develop - from being simple acquaintances to slowly becoming something more. If it's not your main focus, you can probably skip some minor steps for the sake of brevity (carefully thought, since this may leave the reader with that kind of "what-happened" feeling).
Maybe the obvious point here. I'll just add that people tend to behave differently in different contexts, so even your no-nonsense war captain may enjoy hugs in his private sphere - or some other form of showing affection. There must be something in your MC behavior that will arouse interest in the other. It doesn't have to be sexual or romantic interest at first - it could be just curiosity, irony, even disdain.
Being two different species, maybe there are some prejudices on the table. Maybe they both have incorrect or partial information on the other, and they start to understand how those ideas are wrong. Typical sentence: "You're funny/brave/strong/smart for a human/alien race here". From your alien POV, the human female may be interesting because she seems unpredictable (you mentioned how she plays naive, but can stand her ground fiercely).
Another pretty obvious one. There must be reasons why both characters aren't already engaged (with a member of their own kind, also). At least for us humans, our background of romantic interactions weighs on the present, so you may want to take it into account. Maybe one of your character is so fed up with failed relationships that he/she has stopped trying meeting possible partners altogether. Maybe the other MC reminds them of someone they used to know and admire.
In the story I was writing, my male character had lost his childhood girlfriend in a terrorist attack, and that - of course - changed his way of dealing with people even planets away from Earth. Maybe that's too extreme - you don't have to bring the big guns here, if they are not needed: but you probably already have your MC's backstory sketched out, so look at it for ideas.
TL,DR: there may be interesting "hooks" for you to use in your MC's background.
Ask yourself: how are perceived human-alien relationships in your setting? Are they common? Are they frowned upon? Are they acceptable for some people (e.g., let's say humans with a given culture and background) and unacceptable for others? Those questions won't help you start the relationship itself, but may help you understand what your characters will think in the initial stages.
Let's say, for example,. that interspecial relationship are not-so common and are frowned upon by the stricter part of the population. From your description, your male protagonist will probably avoid thinking of an human as a possible partner or love interest up until the very last moment. Maybe he will start having feelings for her, but will dismiss them as deranged and stupid, or be uncomfortable with the idea.
Again, most thing happen by sheer chance or luck. Moreover, someone said that relationships are based upon event, the concept of event meaning "two people interacting together in some way". Put it straightforwardly, they have to be together for some reason. Forced, if the needs arise. Leave them alone in a room and think of how this two may act, with only the other inside. It could be funny, since being from different races/culture they may have different habits and a different way to look at things.
An alien race of mine perceived gender-separated toilets as nonsensical, since every adult being "knows" what happen in there and is expected to mantain his/hers composure nonetheless. In the same story, my couple were to shipwreck on an unknown planet and cooperate to survive (again, you don't have to be so extreme).
In general, put them in situation where they can stick to their "normal" persona and see how things go from there.
Hope I've helped you somehow!
It all depends on the tone and basis of your story. How 'real' or 'sexual' do you want it to go?
If you take something like Star Trek's "pon-far" and trace it back to its obvious foundation you can work forward from there:
Smitten, she tries all her womanly wiles on him with no response - eventually she gives up.
In a convoluted set of circumstances he becomes ill or afflicted some way, apparently dying his behaviour changes. Trapped in wherever - she looks after him.
Believing he's dying He's nice to her. An 'incident' takes place. (Maybe we'll intimate it was a mercy f**k).
He gets better. They are both embarrassed. They agree never to speak of the incident again. He returns to his stoic ways. She attempts to move on with her life. She transfers ships or whatever. He begins to lose his mind.
On her new ship she meets another one of his race, and older female. The female explains that the male of her species exhibit weak (nice) behaviour during mating season, and can be physically taxing on young males experiencing their first season. Once mated, her species are bonded for life and suffer when separated from a living partner.
Broken down: we've that species behave like cats during mating season (gagging for it) and like swans during thereafter (mated for life).
Best I can do - short notice.