Showing her you’re interested isn’t about making you more attractive to her. It’s more about signalling that you’re receptive if she’s also attracted to you.

If she’s attracted and knows you’re attracted, the relationship can proceed.

If she’s attracted and doesn’t know you’re attracted, she’ll either be in the same position you’re in now, conclude that you only want to be friends, or move on to someone who’s attracted to her.

If she’s unattracted and knows you’re attracted, everyone can get in front of their feelings before you feel like you’re wasting your time or she feels like she’d be losing a friendship by not being romantically interested in you. The longer you withhold your feelings from her, the more difficult you can be making things for both of you.

All that said, I think it’s totally reasonable to hang out with her a few times to see if you like hanging out with each other first.