Snapshot to migrate a WordPress website?

Can I use Snapshot to migrate a WordPress website somehow?

We have a new client that had a developer disappear. The developer was providing web hosting for them, but never told them the FTP information, so I'm not sure what the best way of migrating is.

The hosting environment is too restrictive for the Duplicator plugin to properly archive all of their content (times out), so I'm running out of options and the clock is ticking. As of this moment, I'm unsure of the actual PHP timeout and memory limits, as those do not appear to be visible to me.

Thankfully the client has access to the domain name, so provided we can somehow archive the content in a way that lets me download everything, we should be able to re-point the domain name to a new server without issue.

This is a time sensitive issue, so any ideas are welcome. Thanks in advance for your help!