I didn't give him anything (I wish I had at least gotten a card) but I did pay for the breakfast we had during his birthday trip. That was 2 months in.
I ordered a cheesecake from juniors in NY so he could eat like diddy (the place diddy made "da band" walk to) lol, and a homemade red velvet cake that will make you smack yo mama AND yo grandma...gotta fatten him up i guess lol..so something simple and cute
My SO's birthday was four months after I met him, but it also falls near Christmas. (He had already asked me to be exclusive a month or so in).
It was his Christmas and birthday gift combined. I spent all the money on a $50 gift card to Best Buy, but I had my sister (the three of us had met up a few times by then) sign off on the greeting card with me, so the gift appeared to come from both of us (i.e. was not "romantically" associated).
If it were coming only from me, I would not have given him that after four months. I would have maybe taken him out to an inexpensive place for dinner (an ethnic place or Outback or something).