Writing a piece 'in character' means you are expressing the views, reactions, and emotions of the POV with an intimate narrative distance.
The most intimate narrative distance is 1st person. But, 3rd person can be as intimate. It's harder to use effectively but benefits from being variable. Meaning that the 3rd person narrator can simply state a date and a location and the situation that faces the character
e.g. It was 1944 in the New Mexico desert at the absurdly named Trinity, there was nothing holy about this blotch of sand. To the contrary, it would soon boil and froth like Hell itself.
Getting those details in 1st person always reads awkwardly. For instance, how many times do you think of the date or the time or how you are dressed? Those setting details need to be slid in slyly in an effective 1st person narrative.
For third-person, in-character writing, you can start with a distant narrative, then move in close, in steps, until you are inhabiting the character's skin. The opening paragraphs of Stephen King's 'Fire Starter' illustrate this method very well.