Bricks, Masonry, Asphalt and Concrete - changing from a sand base to concrete

last year i had made what amounted to a huge sandbox to lay my inflatable pool over. the pools maybe 15ft across, 3 ft high. sand box extends maybe 3 ft around it. i felt like my house became the sahara last summer, what a mistake. between dogs & kids...im changing it to cement. my question is...can i sort of divide the space up into squares, maybe 2 ft x 2 ft and fill them in as i can afford to buy the cement. well i wanted to use quikcrete, and as i expand it, take away the wood forms, and lay against the last installment of quikcrete. is it possible? i know if i did it all at once, with a hired truck, its probably cheaper. im not able to tackle it all at once. ok...tell me its not possible...
franki