No, this falls under the category of "premature construction," which is explicitly prohibited by Section 319(a) of the Communications Act. However, the FCC does allow certain activities to take place before the construction permit is granted. These include:
Site clearance.
Pouring concrete footings for a tower.
Installing a tower base and anchors.
Installing a new power line.
Purchasing and on-site storage (but not installation) of radio equipment.
Undertaking other preliminary steps that do not have intrinsic broadcast use.
It's important to note that any construction of towers or installation of radio antennas without prior authorization is strictly prohibited.
References:
https://docs.fcc.gov/public/attachments/DA-18-1153A1.pdf