Will baby come early?

I had my 32 week appointment yesterday and when my doctor went to measure my belly she was feeling around and her eyes got really wide and she was like “oh my gosh her head is already all the way down here” when she got really low into my pelvis.

I asked her what that means and she said it could mean that I will got into labor and that I won’t even make it until my induction weeks (between 37-38)

This would also explain why I’ve been experiencing “lightening crotch” and also started getting Braxton Hicks for the first time this past weekend.

Has anyone experienced this and still went a month or so after being told this? I don’t want her to come too early... want to be at least 37 weeks before I give birth.. obviously I don’t have a choice and whatever happens happens but ugh I’m nervous. This is my first pregnancy so I have no idea what to expect.