I just got my masters a few years back, also close to 30, and had a similar experience. as in, I went through a period of applying for jobs for months. Hundreds. I got phone screens from maybe 15. Got second stage phone interviews from 10 or so.
Eventually I had 3 on-site interviews lined up, all with companies I loved in positions that matched my skills. Success seemed guaranteed!
I was rejected from all of them. Crushed. Scared. I had to ramp up applying again and go through the same 3 stage interview process all over. On top of that, I was running out of money. Actually, running out of credit cards was more accurate.
At this point I had been out of work for months. I had graduated school and immediately moved to a hot market, thinking I could land a good job right away. Now I had no money and a three month gap in work history, and no support system to fall back on within 1000 miles.
I started driving for Uber. The only job I could think of that wouldnt look bad. It sucked. I had a ton of student loan debt, a masters, and I was doing a job you can do without graduating highschool.
Eventually I got another round of three on site interviews setup.
In my second round of interviews I got an offer from all three. What changed? No clue. In the depressing down time I got some cool stuff on GitHub, spent an inordinate amount of time making my resume perfect, and studied lists of stupid cs interview questions for days. Going through so many interviews also taught me how to interview to some extent.
It was still a crap shoot and everybody goes through the same unless you've got something like Harvard on your resume.
It's gonna suck but you can do it. It will probably take 50-200 applications to land your first job. It's mostly a numbers game.
At my last company I was part of the hiring process occasionally. About 100 people would apply to one position. 15-20 would have the desired skills and experience listed on the resume. 5 of those would pass the phone screen questions. All of those would come in for an interview and we hired one.
It's a personal example but I feel like it's a pretty average hiring process. From there you can figure out your own odds average case. So on average to get a job: apply to 100 places, get 15 phone screens, around 5 on sites. At this point 50% of the average candidate would get hired.
Keep strong, once you land something this will be behind you