I keep trying to figure out how long the first draft has to be if the essay is 300 words long. Please respond if you know!
As long as it needs to be to get your points across.
There's no formula, saying that your first draft has to cut x% of words.
Plan your essay out in advance; identify your points - write your argument to with the word count in mind, then use your draft to tidy it up.
There's no hard and fast rule, and it depends how many drafts you're thinking of doing before the final version.
If this is the only draft, I would aim higher than the limit. If there will be second or third (etc.) drafts, the first draft is whatever gets your ideas in writing.
[I tend to think of a first draft as a summary, which expands into a longer second draft, which is cut for the third, which might be the final version (but often isn't). I wouldn't do fewer than two draft versions, but that's just what works for me.]
There is no one perfect answer to this. If your process isn't being evaluated, the only important thing is the final draft. Whatever steps you need to take to get there will vary from person to person.
However, if you are writing this for a class and your rough draft is going to be reviewed, then the word count may very well matter. The problem is, the only person who knows for sure if the word count matters and what the parameters are is the reviewer (most likely a teacher or professor). If you cannot ask them, I recommend writing 300 words, just to be safe.
What kind of a writer are you?
I tend to write more than I need, then I hone the work in the editing process. So for a 300 word essay, I would probably first write a draft of 600 words. I wouldn't double every draft I write, it's just that this is super short.
If you're someone who writes a solid outline first then slowly fleshes it out, then your first draft might be 200 words, because you'll add to it in the editing process.
The correct answer though is: The length your teacher thinks it should be.
You should really act like how you feel. There are no specific guidelines for how many words on your draft or what word count. Just write everything, finish it and then start the editing (I’d better wait overnight). See if all the parts fit in the essay and if not, get them out. If they slow you down, then don't write them. It should be fun to write, not restraining you.