What would be a good technical way to go about engaging with a girl who gave me her number over a month ago but I never texted for whatever reason?

I know some would say to move on but I am obviously in scarcity and this girl was actually genuinely cool and we had a real connection that I would like to pursue against the odds of being successful.

I know I got a foot in the door because we made out and talked a lot and vibed really well and at the end she gave me her number without me even asking.

The thing is I've been overanalyzing how to actually invite her over for a date. I would take her to get coffee and then go for a walk in the park to sit in the sun so I think I can manage with the actual date.

What I struggle with is how to start messaging her considering it's been so long. Like the actual words and content. I don't know if I should bring attention to the fact that time has passed, or apologize or whatever I really don't know how to go about this.

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Update

I went ahead and simply messaged her last night and asked her how she's been. Surprisingly, she responded within a few minutes. We chatted a bit and I asked her out for drinks sometime this week. She said yes and even asked me if I had a place in mind we could go.

I already had the "logistics" figured out and thought of somewhere close to where I live. I said to her we could go to this chill bar overlooking the canal and watch the sunset. After that I asked her when she was free. She didn't respond but we were texting around midnight so I assumed she fell asleep or whatever since she was responding in a timely manner.

She didn't open the message until today in the afternoon but hasn't replied back. Judging by this, I assume it's over at this point. I won't pursue her any longer and will just leave it at that. I'm kinda disappointed however because I thought it was going somewhere since she seemed interested. Overall I'm glad I decided to eventually text her but it's my fault for waiting so long. Lesson learned.