Is it normal for her to not text me first ever

She replies to you but never starts the conversation. That's information. It doesn't mean she dislikes you. It means she's either not the kind of person who initiates, she's keeping her options open, or she likes you enough to engage but not enough to pursue. The only way to know which is to change what you're doing and watch what she does next.

Most people assume one-way texting means she's not interested. Sometimes it means exactly that. Sometimes it just means she's comfortable letting you lead. The difference shows up over weeks, not days. If she stops replying altogether when you pull back, that's telling. If she suddenly texts you first, that's telling too.

When you send something, it needs to be worth her taking out her phone for. That's not about being clever or funny. It's about asking something or saying something that actually invites a real response. A dead question like "how was your day" doesn't count. She'll give you a three-word answer and you're back where you started.

Send something that requires her thought. Reference a conversation you had. Ask her opinion on something specific. Invite her to something. The point is to make replying more interesting than ignoring. If she still doesn't text first even when you're consistently giving her things worth responding to, you have your answer.

If she takes five hours to reply, don't text her again for at least 24 hours. That's not punishment. It's creating space for her to notice you're not there. Right now she knows you'll always text next. She has no reason to break that pattern.

If she texts you back and you reply in 10 minutes every time, you've signaled that texting you is always available to her. She can put it off. After two weeks of her not initiating, send her something about once a week instead of multiple times. If she still doesn't text you, you're not her first choice for texting. Decide if that's what you want and act accordingly.