There are two types of girls. Those who do, and those who never do.
Yes, there are girls out there who will NEVER message a guy first no matter what. He could straight up tell her that he's basically in love with her, and she's still gonna be too much of a pussy to message him first. Okay, maybe if not exactly a pussy, just traditional as hell and not willing to let go of those old-fashioned values that the guy always has to initiate the conversation.
I personally belong in the second group = girls who have no problems texting the guy first. If I'm interested and wanna talk to the person, I'm not gonna sit on my ass waiting for hours for him to contact me. I have yet to meet a guy who doesn't like the girl taking some initiative when it comes to talking. I see absolutely no reason not to do that, and I will continue doing so, especially if, as you say, there is a bit of familiar ground. Let's not be silly and play games.
I am currently almost always the one to text first with my crush.. so annoying
I did once, then I repented when he didn't reply back. I really liked the guy so I thought, "poor guys they always have to do the first move, we are in the 21st century, women should start giving signals too, not just the men"... well it failed! I'm never texting a man before he does! FT!!!
I initiate the texting, but only if the guy does at times too. If I am the one always initiating , and he doesn't put the effort in... I assume he is only responding out of politeness and not interested , so I don't waste my time messaging anymore.