I know several people who got full-time gigs at companies you would definitely have heard of with almost no prior professional software experience based nearly

I know several people who got full-time gigs at companies you would definitely have heard of with almost no prior professional software experience based nearly entirely on the fact they went about fixing bugs in commercially supported open source projects. Some hired by the vendor itself. Others hired by people reliant on those projects. Demonstrating initiative, conscientiousness, and acumen are apparently sought after traits. Some in Python, some in Ruby, some in Javascript. What they all had in common is that they'd all been working food or coffee service up to that point, not programming professionally. I'm not entirely sure where the 3 month time limit came from that you added?