Falling blocks can place themselves while riding an entity

If a falling block is riding an armor stand it can place itself on the ground if lined up on the y-axis correctly.
Summon an armor stand with a falling block passenger

/summon minecraft:armor_stand ~ ~ ~ {NoGravity:1b,Passengers:[{id:"minecraft:falling_block",BlockState:{Name:"minecraft:stone"},Time:1}]}
/execute align xyz run tp @e[type=armor_stand,sort=nearest,limit=1] ~0.5 ~-1.975000023841855 ~0.5

then teleport it to be lined up with the minecraft block grid and on the ground and it will place itself.