I downloaded LibreOffice 7.0.3 but it still won’t open with Mac OS 11.0.1 Big Sur.
Will a new version be available very soon?
LibreOffice 7.0.3 does work with Big Sur (e.g. on my system). So there must be a problem specific to your system, but you did not provide any information e.g whether you already tried to run:
/Applications/LibreOffice.app/Contents/MacOS/soffice --safe-mode in a terminal. If that works, your LibreOffice user profile may be corrupt. Additionally you may have not provided Full Disk Access to LibreOffice.app, which also may prevent LibreOffice from starting.
If you want to keep up with new version's release dates - bookmark https://wiki.documentfoundation.org/ReleasePlan.