In theory all of these places could be exploited. I am not going to go into specific exploits available as these change constantly with archive format and moving tech:
Initially downloading and saving the archived data (still packed)
It is unlikely but it is possible that your download manager / web browser does have some kind of exploit. You say the source is untrusted therefore the server could try and attack your download program using exploits in its implementation or weaknesses in the file transfer protocol you are using. These exploits are rare but not unheard of. But fundamentally unless you are certain your software is entirely unexploitable any network connection with a malicious server could result in an attack.
You can somewhat mitigate this by sandboxing the download software with only minimal permissions and access needed to the location you wish to download to and the network stack. This mostly mitigates this weakness assuming your OS permission model or sandboxing software do not also have exploits.
Unpacking the archived data
There are numerous attacks over the years involving using poisoned archive files to run arbitrary code on a system by exploiting weaknesses in the archive format or decompression software. These are probably more common than the above weakness.
The main protections are again making sure to give the extraction program minimal permissions and potentially sand-boxing it to ensure it can do minimal damage if it is attacked successfully. Caveats above apply.
Executing any file from the unpacked archive
This is obviously enormously risky, and the same issues as running and malicious software applies. It is relatively easy for software when run explicitly to break many sandboxes and permission system protections so all bets are off. You can have some safety running the software in a hardened VM but this still doesnt fully protect you short of using an airgapped machine to run the programs which is then destroyed.
All of these steps are fairly risky, but each successive step is probably more dangerous than the last.