Yes! If you can legally possess a handgun, you can purchase a silencer or machine gun, with some caveats that have to do with the National Firearms Act.
You must meet all the criteria for purchasing a handgun, i.e. be at least 21 years of age, proper residency, clean background check, etc.
To purchase any NFA item you must fill out an ATF form 4, similar to the form you fill out when you buy any other gun, and additionally you must have your fingerprints taken and mail the documents plus a $200 check to the federal government.
Once your paperwork is approved (6 to 18 months) you will be given a “tax stamp” which is literally a stamp that you must keep with your firearm at all times (enterprising individuals photocopy their stamps onto wallet-sized laminated cards).
Each new purchase of a silencer or machine gun comes with a new stamp.
Some special considerations:
You can only possess machine guns manufactured prior to 1986, which means they are in limited supply and therefore prohibitively expensive for most individuals.
A short-barreled rifle or short-barreled shotgun (under 16 inch barrel length) is considered an NFA item and requires a tax stamp.
You cannot convert a rifle into braced pistol, but you can take a braced pistol and register it as a short barreled rifle. Once a rifle, it remains a rifle, though.
You cannot let friends borrow your NFA items without your presence.
If you move, you must notify the ATF. You must receive permission to cross state lines with your NFA items.
More information: https://www.atf.gov/rules-and-regulations/national-firearms-act