You need earned income to contribute ROTH

401K withdrawal are considered unearned income, similiar to interests earned from bank deposit. 

It is not earned income that is needed for ROTH. 

Of course you can easily work 4 weeks to earn income up to $6500 to contribute to ROTH, the problem is that you will pay social security tax on it, in additional to income tax.  Let's say you give your child $6500 to "hire" you as babysitter, that's earned income.  But your child as employer has to pay 7.65% social security tax for you, and you have to pay the other 7.65%.  So you and your child has to pay 6500*15.3%=$994 social security tax in order to get $6500 earned income reported as eligible for ROTH contribution.   Actually I think the employer's share of 7.65% doesn't count as your earned income, anyway, you get the idea. 

However, if you only earn $6500 well below the $22850 limit, your social security won't be impacted.  Only earned income above that limit will result in reduction in your social security payment.