There is nothing my child or friend or other loved one could do to make me comfortable with them dating a person convicted of attempted murder and assault with a deadly weapon. There is nothing they could say or do either to make me feel comfortable with them sleeping with a person they've known for two weeks, or sharing a bed with them without sex.
I would strongly recommend that anyone I love get to know someone slowly over a course of time, get to know their family and friends and establish a non-sexual relationship for a good long while before they engage in a sexual relationship. If it's a stranger met at a party or bar or grocery store or wherever, I would hope they would not even get in a car with the person within the first two weeks, much less get in bed with them.
It's good that this man has work but other than what he tells you, you have no way of knowing much about him this soon. What you do know indicates very poor judgment, very low self-control, disregard of the law, and a very volatile personality with no regard nor respect for the security and peace of mind of others.
You need to be aware there is someone out there who is living with the memory of this person attempting to kill them. There's another person who is living with the memory and lasting impacts of being assaulted with a deadly weapon, likely being in fear of dying. If your personal standards for a partner allow you to date someone who would make another human being suffer in fear of their lives and suffer physical harm at his hands, I think you need to look at your self-esteem and standards and rewrite them.
Second chances are great, but you don't have to put your relationships with friends and family at risk for a two week fling with a convicted felon.
If you want your loved ones to support your decisions and accept the men you date, make better choices and date someone acceptable.
