Hey Daniellop1,
Thanks for asking Apple Support Communities about the issue you're having with downloading an installing macOS Big Sur. First, remove any external drives, hubs, external monitors, printers, etc. while download and installing. Then, be sure you are connected with an Ethernet cable, or on a Wi-Fi network that meets the requirements in the following guide. If the issue continues, you may want to try on another Wi-Fi network or with direct Ethernet connection: Recommended settings for Wi-Fi routers and access points.
If you're only able to use Wi-Fi, check for possible interference: Resolve Wi-Fi and Bluetooth issues caused by wireless interference
If you're still having an issue, try installing while started to safe mode to rule out any software interfering with the installation process: How to use safe mode on your Mac
Let us know how that goes.
Take care.