I haven't intentionally started strawberries from seed either. But FWIW, two winters ago, I noticed a tiny strawberry seedling starting to grow in a container of another plant. I believe it may have grown from a whim experiment -- strawberry seeds left in the bottom of a home made strawberry smoothie (frozen home grown strawberries from previous season) that I scratched into the soil.
I took care to put the plant in a cool window to help the baby strawberry plant, and in spring, I separated it and potted it up in its own pot. I set it outside in my kitchen garden where I could keep a close eye on it and it grew well through the season. After its second winter, this time outside, it has been producing flowers and fruits this spring.
Sometimes, I see strawberry seeds of varieties specifically described as "will bear fruit this season". I believe they are supposed to be started in January. So I would infer that most strawberry varieties will NOT bear fruit within the same season they are started from seed.