No although it might start in Feb rather than Jan. It might depend on if you had the payment from elsewhere in Jan. 
It is only one payment of course each month and gets paid like this 

Sofa surfing for 6 months. So had no other payments!!  Fingers crossed maybe get this months 

It doesn’t sound like you’re eligible for the EBSS payment on that property for January, because you weren’t there on the 1st January. You will qualify for the ones for February and March though.