Strawberry straw

G'day all, I've cleared my strawberry patch of last years straw. We were a bit late putting it down & had to lift a fair bit of fruit out of the way and tuck it under the plants.
The plants are all healthy looking with plenty of new growth coming. When should I put new straw down. Can I put it down now so the plants grow up and over or will it restrict it's growth.
Thanks.

Br