She seems unsure about our future

I have been trying to explain to my girlfriend that we need to get serious about our relationship if we want to get a sense of what the future looks like. We are both in our early 30s and while there is no pressure from our parents, I think it’s time to at least consider whether we want to get into a long-term commitment. We have been together for four years and I am pretty sure this is the person I want to be with. I know she feels the same way, or she wouldn’t have been with me for so long. The problem is, whenever I talk about commitment, she makes it feel as if I am trying to tie her down and curtail her freedom. I don’t understand this because it’s not as if she wants to date other men. Should I just let things stay the way they are indefinitely? I know there will come a point when we won’t be able to put this off any longer, and I don’t want to keep going through life not knowing if we have a solid future together.
As you point out, there will come a time where either one of you may feel the need to commit to something or define where this is going. It’s okay if your girlfriend isn’t at that place yet, because the two of you are together and are happy, which is all that should matter for now. You have told her how you feel, and she has been clear about her misgivings. The best thing to do is enjoy each other’s company and companionship until you get to a point where that isn’t working well for you. Giving her time to arrive at this place on her own is the most sensible thing you can do.

How can I convince this girl I am dating that I am genuinely in love with her?
You can tell her how you feel, and maybe focus on your actions along with those words.