Actually, a solid fueled Saturn V first stage was considered with multiple prototypes built and fired:

"The largest solid rocket motors ever built were Aerojet's three 260 inch monolithic solid motors cast in Florida.[18] Motors 260 SL-1 and SL-2 were 261 inches in diameter, 80 ft 8in long, weighed 1,858,300 pounds and had a maximum thrust of 3.5M pounds. Burn duration was two minutes. The nozzle throat was large enough to walk through standing up. The motor was capable of serving as a 1-to-1 replacement for the 8-engine Saturn 1 liquid-propellant first stage but was never used as such. Motor 260 SL-3 was of similar length and weight but had a maximum 5.4M pounds thrust and a shorter duration."

and

"Between Sept. 25, 1965 and June 17, 1967, three static test firings [of the AJ-260 rocket] were done. SL-1 was fired at night, and the flame was clearly visible from Miami 50 km away, producing over 3 million pounds of thrust. SL-2 was fired with similar success and relatively uneventful. SL-3, the third and what would be the final test rocket, used a partially submerged nozzle and produced 2,670,000 kgf thrust, making it the largest solid-fuel rocket ever."

For more see: https://en.m.wikipedia.org/wiki/Aerojet#Florida_facility_and...