No, not my first use by a long shot. I do all my cooking on the cooktop. Don't be too nervous about using it.
I knew that HollowHill had her cooktop split, and so was a bit leary, and being careful not to add fuel to a good fire, which is what she had done, immediately before hers split. I don't think her stove was very hot either.
My theory is that both our stoves just had a rapid elevation in temperature in a very short time, as opposed to reaching any particular temperature. I was trying (unsuccessfully) to avoid that, after HollowHill's experience.
My son was not at all surprised about HollowHill's cracking, when I told him. He had installed my stove for me, and he said that the cooktop had way too much exposed surface to be able to take the rapid heating and expansion without cracking, because of the surface area the flanges on the bottom add to the cast iron cooktop lower surface.
Cracking at 300F doesn't sound like the stove was being pushed too hard or too fast. This sounds like a design flaw. Your son may be correct. If different materials are expanding at different rates and there is not enough room for this expansion, something has to give.