Should I greet him on his birthday?

Hey girls.
It’s been 2 months since the split, and I know it hasn’t been that long, but I think it’s slowly getting better. I can sleep peacefully without crying my eyes out. I haven’t contacted him for 27 days straight now. Though me and his mom talked thrice this month. There are still days where I feel heavy and I miss him badly. But there are random moments I think of him and all I remember are the happy days and it makes me smile. I think it’s a good sign, right?
Anyway, it’ll be his birthday soon. Which was also supposed to be our anniversary. Do you think it will be a good idea if I greet him on his birthday? He still hasn’t reached out to me since the breakup and I don’t want to ruin his special day because he got a text from me.