Sounds like a tricky situation and I can feel you- although I never had this situation so far- but I remember the feeling of being all hyped up to reach a place because crush will be there- even if it wasn’t „mutual“ and I was only fangirling…
How well do you know each other- do you know more than each others name? Do you know personal information like hobbies/if he has a pet- what kind of food or movies he likes? If he likes to go clubbing owl through the night or rather prefers a walk in the sunny daylight?
I am asking this because the question is- how serious you would like to have it- or how deeply he might care for you! In the end- if you find out it is all about playing only and you „wasted“ your time in hopes and dreams that didn’t lead to anything you might feel betrayed.
So in case you are interested in growing the contact into something real, not just merely shy, muted, eye contact- and only know little about him (which of course males it all the more interesting at the moment) but you (both?) are the introvert type- try to find a cute playful way to let him receive a message (preferably not digital)
Do you know what kind of snacks he likes?
If so, you could try to think of ways to deliver it to him including a little „anonymous“ note without anyone knowing it is you- do you maybe have friends who could place it there so you won’t be seen by his friend?
Another possible way to get in touch with him/get s conversation started that is not as sneaky as the snack w/ note idea would be to throw a comment that is designed for a situation you might be in st the same moment, maybe if you „accidentally“ meet him somewhere>>
maybe when heading for lunch break, or when you notice he just left the room you could act like you need to make a quick a phone call or something which makes you need to leave the room a minute later or so than him - and chances might be to run into him on his way back you night just say smile to him and say hi ,
same if you decide to leave the room next time because you want to get a snack and stand full of indecisiveness infront of the snack machine- maybe he will ask what’s up!
You could also act as if you don’t have the right coins and search through your wallet for some time after previously „preparing“ it with mostly small coins/big bills the machine wouldn’t take..maybe he offers to help you out!
Or as previously mentioned if you should be lucky to meet him in lunch break you could male a comment about the menu or ask if he has tried this and that yet…or say you still haven’t decided which one to choose etc..
The goal you want to be heading to with moves like these should be to maybe meet up for a coffee date one day- having lunch together would be a great start- you could also recommend a place if you see he really eats xy quite often and say sth like oh have you ever been to that place? You MUST try it!
(For this idea of course you should choose a food place that isn’t too famous yet in your area/just opened/ has mostly good reviews and maybe something original on the menu- maybe you want to „show it to him“ when you found out he likes a certain type of food you might be saying something like - oh you like xy? I hear of that place that just opened/is known for having awesome… would you mind to join me ?
I don’t know in which work environment you are set/ if these tips could be realized at all but maybe it is helpful in some way :)