I’m in zone 3 in Canada. I feel your pain! Have you ever heard of “grow bags?” Check these out: VIVOSUN 5-Pack 20 Gallon Plant Grow Bags, Heavy Duty Thickened Nonwoven Fabric Pots with Handles https://www.amazon.com/dp/B00VWU2UDC/ref=cm_sw_r_cp_api_glt_fabc_DJ7P1273QGRRC96CMM80
Yes you can grow strawberries, but if you were hoping from seed you’ll have to plan for next year. Some strawberry seeds need to be frozen first!
I can’t really tell if you have one already, but If you’re in a colder climate, putting a heating mat under this will vastly speed up seed germination.
https://www.amazon.com/dp/B00P7U259C/ref=cm_sw_r_cp_api_glc_fabc_J8caGbJCFE779
My biggest mistake though was seeding too early in the year. I usually start around March. It is very easy to run out of space before the season warms up enough to move everybody outside.