I'd ask them out pretty early on tbh... you both know why you're there.
I think while it might be good to ask a few questions about them initially to find out about them personally, what their interests are, what they do for a living etc..etc.. beyond that you ought to just meet them rather than drag out a conversation with stuff like "how was your day?".
A first date can literally be something as simple as coffee - you're doing each other a favour there as either of you could decide that you're not right early on without wasting half an evening and a wad of cash on dinner or several rounds of drinks or movie + drinks + popcorn etc..etc.
someone I know lined up several dozen dates for coffee, she spent weeks doing this, she'd basically message people, arrange to meet up and then just meet them for coffee at lunch... you can often tell fairly early on whether you click with someone or at least whether you definitely don't click with them. If she didn't like them then she'd drink it quickly and head back to the office... literally just takes 15 minutes of your lunch break to do that.
She was able to get through a whole load of dates until she found someone who ticked all the right boxes... and is now married to him.
This is a thread we can agree in