It depends on what part broke. If above the true leaves, survival is very likely with new shoots growing, if above seedleaves but below first true leaves possibly, but if BELOW seedleaves, not likely.
Cucumber is very easy to grow from seeds. Try getting some seeds of types you like and try sowing some. If you soak and pre-germinate like I've been doing, the first root tip starts growing within 48 hours and you could just sow those living seeds.
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