I agree with @DarkestKnight , in that I would be somewhat careful so as not to damage a likely already fragile self conscious and confidence system.
I would however, considering doing work to get closer to her in the meantime.
I do not mean romantically, intimately or sexually but rather as friends.
I suggest this because, for the second time in my life, I have found myself to be in a relationship with my best friend.
The first time, the man I was with became my best friend. That was pretty great, things worked well but we humans have a way of letting things that don’t matter come between us.
My current relationship, is with the man I spent time with prior to becoming involved with. It was only ever meant to be friends, but by the time we hit six weeks of spending every single day together, including when I had my children, his grandfathers birthday party, his moms families dinner and all kinds of things like that prior to even considering a sexual or romantic relationship… well.
Eventually be both had a moment where we said wait a minute, pay attention dummy or your going to miss it… because it was a deeper thing, with more potential than what is right and fair and all.
End ramble. Sorry TLDR: Consider developing a purely platonic friendship with the woman first. The relationship will likely be more rewarding in the long run and it will give you time to determine if there is true chemistry and potential for a long term relationship that will check most of your wants and needs, or perhaps determine if regardless of what you currently know, think and feel about the woman she either needs more help, support and possibly therapy to overcome her traumas, if your willing to go through it and aid the process and of course, it will also help you to discern if you’re truly compatible.
Close friends often do many of the same things together that a couple also would-such as watching movies, spending a day at the beach, video gaming, going to the bar and so and so forth.