Legally, it depends on the country, but in most countries, it is impossible. However, you can start with someone else’s name.
On the other hand, if you are talking about possibility in terms of time, money, etc., then the answer would be yes you can!
Working hours in the government sector are from 7 am to 2 pm which is a short period, then working in the company from 2 pm to 8 pm. You will be you energetic and passionate because you will be working on your own business.
Meetings can be postponed to 2:30 pm by letting clients know that you have other meetings in the morning, which will make them respect you because you are busy all day.
For me, I’m a government employee, and I have owned many companies for ten years without having any problem managing them.