Somebody at work told you about the backdoor Roth. They were excited. They used the phrase "totally legal" at least twice, which is usually a sign that something is about to get complicated.
And they were right, it is totally legal. It is also, for a large share of the people who try it, a small disaster, and the reason is one paragraph of the tax code that nobody mentions at happy hour.
So here is the honest answer to the question in the title.
Yes, you can. You probably should not, until you deal with the existing IRA first.
Because the IRS does not let you cherry-pick which dollars you convert. It looks at every traditional IRA you own, blends them together, and taxes your conversion proportionally.
That rule has a name, the pro rata rule, and understanding it is the whole ballgame. Let's take it apart.