I had a firearm restriction on my background check, since I was 15 yrs old. I didn't know until I went to purchase my Glock this past February. I am now 22, so in those 7 years I have not had any law enforcement contact and have been free of trouble.
I had to contact the CIB (crime information bureau) to find out why. 2 weeks later they sent me a list of offenses I had when I was a juvenile and one was OWI hit and run causing injury to a minor, class f felony I believe.
I was drunk, crashed into a tree and my friend was the passenger and hit his head on the windshield causing a scratch on his forehead. I took off and was subdued a block away. I was 14 turning 15 and a dumbass.
I have change my ways of living and thinking since then.
Back to the process, I then wrote the judge, who replaced the judge that handled my case and asked that she lifted the restriction. I gave her details as to why I wanted to own a gun and how I have changed my life since then.
5 days later I received a letter with a court appearance date. I attended the hearing and was granted my rights back.
The total time, from when I started the process until I was able to purchase the gun, was 2 months.
This is in WI, and depending on the reason you have restrictions may play into a longer waiting period.
My brother went through the same process and didn't receive a letter from a judge for 6 months. Then they told him they wanted him to wait a total of ten years from the original case date, without any police contact, which was 3 more years.
Good luck