They might survive but the odds are against it. Both do much better when direct seeded as they don't tolerate transplanting well even under ideal conditions. If transplanted it needs to be before the 3rd true leaf develops.

If you have the space to see what happens with them fine. Otherwise I would pitch them and just direct seed them at the proper planting time.

Dave

Normally, I agree with every common sense word digdirt writes and I also agree that it is probably best to start again with your plants. However, this bit: "they don't tolerate transplanting well even under ideal conditions. If transplanted it needs to be before the 3rd true leaf develops" is not imo strictly accurate under all circumstances. In cooler climates, like mine, squash are routinely transplanted. If direct sown it would well into June before the ground was anywhere near warm enough for them to germinate and even then they'd need sowing under a jam jar or cloche. As it is I will put mine out in mid May with some fleece protection, having started them in my glass porch 2 weeks ago. At the moment they are being hardened off. And they are often well past 3 true leaves before they get set out. You could cover all bases by starting new ones and setting out the old ones, just to see how they do.

I started 3 squash seeds in mid Feb although My zone is 5b. I did this because I was wondering if the acorn squash I had for dinner had viable seeds. Normally I plant squash at the beginning of June, outdoors so by the time they come up, the squash bugs have already passed my house. Since the seeds are growing, fast, I figured that I would keep these particular plants in the sunroom, give them names and hope for a early crop from them.

I have to agree with floral. Around here in my cooler zone, squash and cukes are regularly started in pots and transplanted... and do really well. I've started my own, and bought them from local nurseries too. It is usually better to plant them in a bit younger rather than older though. I've lost late season/overly mature seedlings picked up from a nursery way more often than planting in younger seedlings.

But more to the OP. If you pot them up well and give them good light, nutes, and water, they should grow fine. After all, people do regularly container grow squash and cukes with success. However, I would advise to just pot them up in a larger container and keep them in the container rather than trying to transplant them again into the ground. Trying to transplant them when they are too mature can make them go kapooie.

I did this last year not knowing what I was doing... don't waste your time, just pop some fresh seeds in the ground in May, and they will grow like crazy, much faster than any attempted save at the seedlings. Started in February, they will be weak, spindly, rootbound plants, flowering in the pots, that are unlikely to transition well to the garden. Squash family are fast growing. They will also go through crazy amounts of water and will be difficult to keep alive.

Re transplanting, I did buy one Zuke transplant at the store, and it transplanted fine. But it was small. Then again, the seeds I planted in the ground next to it caught right up and even maybe grew a little faster.