Is it fine to ask my advisor if I can appear as first author in our paper?
Yes, of course you can ask, and give the reason. But it may be moot depending on your field. In some fields, alphabetical listing is the norm. In others it is vitally important and fought over.
If you are in a field in which it is important, then I hope your advisor is a bit generous in this since you are starting out. But if you aren't the main driver of the ideas in the paper then you should be prepared to yield graciously. Other papers will come. Your first paper isn't, hopefully, the best work you ever do. There will be future opportunities but they depend, somewhat, on cooperation with others. You can also be generous. Especially if you are willing to take a long view.