As you say, 25 is not old at all. As long as you keep socializing with friends and coworkers, pursue IRL hobbies ideally social ones, etc. as you mention, I don’t think it matters much if it takes you 6 months or >5 years to reach your fitness goals.
The only people I’d consider “”“lost cases”“” I know personally are shut-ins who have long mentally parted ways with baseline humanity. An inability to have a decent conversation with people is harder to fix than being overweight and becomes more of a problem with each year of age. But you seem to be on the right track there!