It would bend or stretch before it snapped. Nearly all, if not absolutely all, materials that you might want to build a see-saw from will deform before they snap. Maybe it won't deform much, but that ok, and is enough to transmit a push from one end of the lever to the other.
Remember, a lever is just a collection of individual atoms linked together by elecromagnetic forces. You push of the atoms on one end, and they are going electromagnetically push on nearby atoms, and that push is going to propagate as a wave at around the speed of light.
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It would bend or stretch before it snapped. Nearly all, if not absolutely all, materials that you might want to build a see-saw from will deform before they snap. Maybe it won't deform much, but that ok, and is enough to transmit a push from one end of the lever to the other.
Remember, a lever is just a collection of individual atoms linked together by elecromagnetic forces. You push of the atoms on one end, and they are going electromagnetically push on nearby atoms, and that push is going to propagate as a wave at around the speed of light.