Predicated on there already an Older Version of Ventura being installed on this computer.
Details of above,
If this computer has, say Ventura 13.2.1 presently installed on this computer.
As Safe Mode is not working to install Ventura 13.3.1 >>
There are factors:
1 - Like poor Wifi connection
2 - Slow wifi connection
3 - Too many other people downloading at the same time and Apple Severs are overloaded
4 - Software on the computer interfering with the download process including AntiVirus Software
Notation: Disabling the AV Software may or may not solve the issue. Removal of the AV Software may increase the chances of the download to perform as expected.
5 - Running behind a VPN which may increase Packet losses or corruption of the download
6 - If via wifi too many Other devices using the wifi at the same time reducing the Bandwidth to your computer.
7 - Best Results are via Ethernet Cable to Router
8 - Worst case - Restart in Recovery Mode and choose Reinstall macOS.
This in theory will pull the latest version of Ventura available and commence the installation.