I'm interested in a girl at work but she's not given me any signs she feels the same way. Should I ask her out?

Just to clarify, even though I work with this girl, the place is huge and we only have a few weeks before she's moved to a completely different part of the building. (Plus with working from home half the time, I'm almost certain never to bump into her, so awkwardness won't be a problem).

Anyway, this girl is younger than me (I'm 34, she's 22). We started at the same time about 6 weeks ago. We've chatted here and there but nothing much. The longest we've spent in conversation was last week when she asked me for help. Beyond liking the occasional meme I post on Teams and laughing at a couple of my joked, there's really been no suggestion that she's attracted to me.

On a whim, for valentines day, I left a rose on her desk. She was flattered and she and her two friends are trying to figure out who put it there but the thought appears not to have even occurred to them it could have been me which I took as a bad sign.

S you can probably tell I've been out of the dating game for a long time now and I'm honestly at a loss about what to do. Should I keep up the secret admirer routine for a bit? Do girls always drop hints if they're interested? A few of us are going out for a drink after work one night - should I wait until then, see if we get along and then ask her out? Or should I just throw caution to the wind and go for it right away?

Any help or advice would be much appreciated. Thanks everyone.
Updates
+1 y
A woman I work with said they'd guessed it was me before I even got there. She also said she keeps looking over in my direction. Of course that doesn't necessarily mean anything - she may just be trying to figure out who sent it.
I'm interested in a girl at work but she's not given me any signs she feels the same way. Should I ask her out?
Post Opinion