Make sure to stay focused on what you can control. I think your optimism is good and you're probably right, you likely have plenty of room for improvement (I did look up your times).
For cross country, that work starts now. You need to take another step forward with your training over the summer and carry that through into the season. Talk with your current coach and consult some online resources on your own and agree on a plan. This will likely be a gradual build up in mileage over the summer. I used to do 4 week cycles with small increases in total mileage each week for 3 weeks and in the 4th week I'd back off a little from the peak in the 3rd week to give my body a bit of recovery then repeat until I got to my peak mileage in the build up. In addition to base mileage, I'd mix in a weekly long run and harder workouts like hills, a summer road race for fun, fartlek, etc. A good summer and strong fall of training and staying healthy will result in faster times. Listen to your body and learn the difference between sore and hurting.
The NC A&T coach probably looked at your times and saw you were a bit outside of where he would expect an athlete ready to compete for his team so only responded with his expectations for what could help the team. If NC A&T is the school you want to be at regardless of running, then let the coach know as your training and racing progresses and let him know that you're realistic about where you are relative to his standards. He may have strict limitations of program size due to title IX or other funding limitations, but if you are already on campus anyways there is no harm in continuing to demonstrate improvement with the hopes of joining the team in the future. There are likely some road running clubs nearby at least you could train with to help your progress.
If you are set on running in college for your school, then there are plenty of other college teams that will be interested in what you could add to their program if you get some solid improvements this year. Division 2 and 3 programs have a wide range of standards for what they allow on the team. Some schools do not have any cut off for joining the team, they only cut the numbers down for meets meaning you might only get to race once or twice at a home meet depending upon your ability. Cast a wide net of schools at different athletic levels that you think you'd like going to even if you didn't run for the team and look into those teams too. You might find a better fit, you might not. Either way, train hard, train smart, and stay positive about your running experience.