Props for wanting to compete! As for timing to be ready for a fight, it depends on alot of variables. Many of them depend on the fight promotion and how you're matched up. I've seen very good wrestlers start within a month or so and win. But these guys were matched up in a good promotion that wasn't shady. There are alot of promotions that throw newbies to the wolves to benefit "their guys".
Your wrestling shaves off alot of time but it sounds like you're very one dimensional which can be very bad these days. IMO focus on striking and cardio for a few months then discuss with your coach.
Best of luck.