Speaking as a women who met my mums new “boyfriend” every time she decided to drop in on our lives (random intervals at best) I would have been happy if she had spent even a month with them before bringing her new man around. But it didn’t really cause me too much grief as I had my Grandparents - they raised me, my brother and sister so, whilst they were far from perfect, they were our stable (using this word loosely haha) family unit.
DH has a Step Father and for a time had a pseudo Step Mother in his Fathers GF. He met both in a relatively quick turnaround at the age of 9/10. His Mum has been with his SF for 24yrs, his Dad split from the pseudo SM after 2 years. This didn’t impact him as - despite getting to know her, he still had his Mum and his Dad for stability (even though they were separated).
What I’m trying to say is, only you can judge when you feel the time is right @HatRack and only you know your DP. If he is a conscientious and caring man then his willingness to introduce you wouldn’t concern me. But when it feel right for the both of you. Use your best judgement and I would say a ‘neutral’ ground area is best as PP have said, go to the park, it’s not massively flashy so won’t set an expectation of always doing planned events when you’re together. As for how long to be there, I’d honestly say 15-30 minutes unless you hit it off well then stay a bit longer. If it’s really awkward you can then leave DP and his kids to play together for a bit?
You’ve said they’re excited to meet you, so obviously they know what your relationship is with their Dad, so that’s the first part already done.
My mum finally settled down with my now Step Father after years of a new fella every few weeks (just to say she’s grown up a heck of a lot lol).