It's hard to assess how appropriate it would be for outsiders who do not know the local customs (and live in a different part of the world). I'm certainly an outsider, but I hope that I can help you find the answer to your question yourself, based on the information you provided. This is about both, you and her (or your future relationship to her and your colleagues).
- You have a crush on her
- You never interacted with her
- You work in different teams
The important question you need to ask yourself is, whether you would want to give that gift to her, if you didn't have a crush on her?
You noted in a comment
I would give a gift to every female colleague in my team, that I interact with on a daily basis, she would be the only one outside this circle
This means that you would single her out. And you'd do so publicly with the gift on her workplace.
She doesn't know you and can't read your mind, but it would not be hard to infer from this action that you have some kind interest in her (note that even if your intentions are innocent and you are the nicest guy possible, she doesn't know you nor your exact intentions). But you are a stranger who kind of happens to work in the same building, and that's it.
I don't know her and don't know how she would react or feel, but you mentioned something very interesting:
Also, she seems to be ignoring me, but I think she does that with all people she doesn't know.
Like that gift would show your interest in her, her behavior towards you (and people she doesn't know) shows her lack of interest in you. It seems safest and least selfish to respect her wishes. The gift, on the other hand, seems very risky
- explicit (it won't go unnoticed, that she's the only recipient outside of your team)
- public (there may be even be gossip about your actual relationship to her, perhaps it's not as unilateral as it seems they may think/say)
- forcing (perhaps she'd feel that you want to force contact between her, even if it just means she'd have to tell you she didn't want further contact with you)
Indeed, it could become awkward for you. But it's highly likely that it will also be awkward for her. We do not know her background and her past experiences and they may have an influence on how she sees it (she could have been secretly in love with you all the time and be overjoyed, but she could also have been stalked by man before and be terrified etc.). Whether it'll already be considered harassment where you live, I don't know, but even if it isn't, it seems too much and too early.
As others already have noted, romantic relationships at the workplace are problematic. You may ask yourself, whether you want to pursue this further. And you do not even know her. If you really want to, slow down considerably and maybe start with a simple greeting in the morning. Also maybe get to know some women who are not your colleagues - perhaps there are some who show more interest in you.