Your "partner" didn't tell you that he has a child, which is not only sleazy but an indication of his sleazy character-
if it worked this time, it might work again, & you could have 2 "surprise" stepchildren, or your son might be the "surprise" stepson of the next woman to come along.

He "does't think it's a big deal".
See above.
& really, seriously, not a big deal?
If son #1 isn't a big deal, how big a deal is your son?

Your child was planned:
This guy knowingly, deliberately *got you pregnant* while keeping a very big secret that surely would have had an impact on your decision to have a child with him.
manipulative, disrespectful, low, nasty, creepy.

He says he planned to tell you (uh...when?), *but he didn't* because he knew you'd have left.
so, knowing the situation would be unacceptable to you, he decided to just not let you know what the situation was.
not a decent way to treat anybody, let alone someone who thinks she's found a life partner in you.

He lied about where he was going when he went to the birthday party, which is actually more than one lie.
It tells you that he lied when he said "not a big deal" (then why lie?) & he lied when he said he "was going to tell you" about the baby (the child was a year old & he still hadn't told you, & he lied to keep you from finding out, ergo...he wasn't going to tell you. ever.)

& you've heard his version of events;
it would be interesting to hear what he told the other mother (now, really, would someone deliberately get pregnant because the guy had money & then genially hand over custody to the father? maybe, possibly another lie?), & it would be interesting to know what he told her about you.

Leaving this miserable situation might not mean you'd have to support yourself & your child alone.
You need to consult an attorney;
I'd bet that this father has financial obligations to his son, & maybe to you as well, especially if you've been a stay-at-home mom/partner.

& remember that treachery is nothing new;
you may feel stupid right now, but guys/girls/partners/people have been doing dispicable things to their nearest & dearest, & then accusing their nearest & dearest of just being stupid, for a long long time.

Put this in the past, & leave it in the past, & go on to live your life & raise your child in a happy, healthy, fulfilling way.

I wish you the very best.

Trust me, if lying/cheating to your spouse was grounds for having full custody of your kids, I would have taken them away from my ex wife years ago...but in this country, or at least in NY state, the behavior in the marriage has little or nothing to do with how custody would be awarded. All that matters if the ability to be a good parent...in theory, anyway. But I know that you just can't take your kids and run away...the law protects against that.

Good luck with whatever path you take....