Probably worth noting that it can both burn you chemically and from heat, albeit at different stages of curing. I made the mistake of mixing concrete with my bare hands for testing specimens in a lab at GA Tech (.41 w/cm ratio with a good amount of class C fly ash, ended up about 6 ksi compressive strength after 2 weeks of curing in a fog room). For those of you who don't know, concrete is a pretty strong base(I suppose this could be a pun) with a pH of anywhere from 12.5 to 13.5, needless to say my hands felt very slippery once I washed the wet concrete off and then were very dry for the next few days. On the plus side, I'll never forget that concrete has a high pH.I can immediately tell they have no idea what they are in for, before I unload anything from my truck I give them concrete safety 101, which is very simple, protect yourself, and don't get it on you! it can burn you.
Also, to answer your original question about what problems could occur if you use the concrete too soon, you could apply a load that puts the concrete past its yield strength since concrete doesn't gain full strength until a full cure. Going past the yield strength would typically result in cracks, which even at a full cure would drastically reduce the strength of the concrete.
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