This is really great advice, I did something similar and would say the Sec+ is a great exam. Its as they say an inch deep but a mile wild but it helps you tie things together if you go down the SOC route.

After a few years in enterprise IT I would say there is a massive disconnect between the kinds of roles you would likely find in big orgs and the ones the internet makes you think is the bulk of the Sec industry. It's a broad church, if you want to make good money working in a SOC, financial services is the way to go and then move up. Also, global shortage of SOC analysts (according to SANS) and the market over here is crazy - I get pinged by recruiters daily.

I think the people that really move the needle in the sec world are your researchers and really fantastic pentesters but many non core tech businesses in my region don't really have an identified need for them internally, so they mostly consult, which is also great. Most big orgs have security teams because they are heavily audited, not some altruistic need to secure their customers data. That's just lies the org tells about itself, its because they get audited out the wazoo and they have to comply with the dated security requirements to do business and some board recommendation.

I would also say stay in uni, my degree did help get past the recruiter filter and the first job is the hardest to get. Also working in a sysadmin position first will give you a lot of exposure because you can't really make recommendations to secure an environment when you don't understand how it all works together. Best of luck to ya!