Equality of opportunity does not rule out a proper socialist system. You give everyone the same opportunities at life and work by e.g. affordable health care and insurances for everyone, but also scholarships for everyone so they can follow what they want to do instead of be restricted by e.g. what their parents earn. And if you can't work because of whatever reason, you don't have to end up on the streets.

Equality of opportunity gives everyone the chance to graduate university; equality of outcome gives everyone a university degree regardless. I'm probably misinterpreting it.

But give everyone the opportunity, and there will be enough social mobility so that people now born in poverty can grow up to become e.g. software developers, and pay that little equal opportunity was paid for them during their education back tenfold within just a couple years of working in that industry.

That's my experience anyway, my dad was a not-greatly-paid metalworker with a high interest mortgage (as was the times back then) and three kids, I'm a college graduate and my first job paid almost as much as his.