I suggest that you first check if the printer is AirPrint-compatible or supports IPP (Internet Printing Protocol). If it does, and you're on the same network as the printer, macOS might allow you to add it without requiring admin credentials. Go to System Settings > Printers & Scanners, click the Add Printer button (+), and see if the printer shows up in the list. If it appears as an AirPrint or IPP device, try selecting it and adding it.
If that doesn't work, you’re going to need to loop in your IT department or whoever manages your Mac’s admin rights. You could ask them to pre-install the printer or provide temporary access.