'Freeze your eggs' is a phrase thrown around by people who've never tried to. It isn't recommended, or particularly successful at your age and above. What is done is IVF, either with a partner, or donor sperm. Embryos can be frozen.
But do remember that stats on people struggling to conceive older, include all those people who've been struggling for years and are still struggling, while their peers have already succeeded. If you're trying for the first time at age 35-39 and are averagely fertile, you may find you conceive quite easily.
You can go to a fertility clinic and get your eggs counted (painless scan) and blood checked out, if you want facts and reassurance.
At your age, I would give it two years of dating (fairly ruthlessly) but also of getting on with your life, doing things you enjoy and having fun. Because it is a cliche but also true that life often happens while you're trying to do other things and, just because it will make you feel better and more 'you', so you can move forward intact and ready to face the next thing, not drained from the dating battle.
Then I would get ready to think seriously about donor IVF etc and take a year to set those wheels in motion, if that's what you want. (Without dropping out of life or dating). Some people are able to parent alone, others would only ever do it with a partner. Both are normal and good.