Maybe. The deadline to recharacterize an IRA or Roth contribution (to the other) is October 15 if you filed your 2018 taxes by April 15. You would amend your taxes with a 1040X.
But I wouldn't be fighting this. This is a Very Good Thing.
IRS is infinitely patient and their interest rate is 6%. This is way, way, way too soon for IRS to send postal mail about your 2018 taxes. If someone is time-pressuring you, it may be an IRS scam; it's certainly so if they are outreaching by email or phone. (IRS only contacts by postal mail). Scammers hit everyone, claiming you have a tax issue; it just so happens you actually do. IRS is very, very slow. It can take them a year to even contact you, and another year to even start with the telephone. And they only ever want paper checks mailed to the official addresses.
If you are pressuring yourself because you don't know what the consequences are and fear the darkness, relax. It's not that big a deal. The IRS doesn't even mark your credit report.
If I were in your shoes, I would just make the IRS wait. The Roth conversion is such a huge win for anyone under 45 that I'd accept a few postal mails.
The 401K is analogous to a traditional IRA.
The Roth is a far superior type, especially for young people.
Here are the differences:
In a IRA/401K, you use "pre-tax money" and put it into the IRA. You've never paid taxes on this money. The money is invested and compounds. At 7% a year in stocks, it will grow by 3000% (30 times). You pay taxes on IRA/401K money when you take it out. And it's 30 times larger, *so that is a LOT of tax**.
(Granted, you pay the tax going in or going out. And that part at least is a wash if everything goes right; modulo some very serious risks.)
In a Roth, you use "post-tax money" and put it in the Roth. You already paid taxes on this money, so it's tax-free when you take it out. Thanks to Senator Roth, the compounding is also tax-free. That is huge. That is the biggest giveaway in the entire tax code. You paid a measly few grand of tax 50 years ago and now you're homefree.
What you did was equivalent to
- convert the 401K to a traditional IRA (no problem there) then
- convert the traditional IRA to a Roth. (super, but gotta pay the tax).
But remember, 401K/Trad. IRAs contain money that taxes were never paid on, and the tax must be paid coming out. That can be much worse if you take it out in a big surge e.g. due to metical issues. Roths can only be funded with money that you had paid taxes on. Therefore, you do have to pay the tax on any money you convert from Traditional to Roth.
This lets you exploit a variety of Roth features/effects. So this is a win for you overall, even if it can be a pinch today. I mean everybody'd rather not pay taxes. But if you have to pay taxes, better a few grand today than $100,000+ when you are in retirement and on a fixed income. (I mean emotionally; it's a wash if everything goes right, but it might not.)
The Roth is a good thing.
Just in the future, try to rig it so you do the Roth conversion in a gap year or years, so your taxes are lower during the conversion. That's another Roth hack :)