your_command_here | less
It will capture the output and let you scroll up and down.
Otherwise, this would really be a feature of the terminal, and not necessarily required to be supported (it makes sense when you consider that many early real terminals literally printed the output to paper -- who needs scroll-back, just look up the tape! And repeating previously shown output would result in a confusing print-out).
However, if your terminal emulator doesn't have a scroll-back, you could try something like tmux, or alternatively gnu screen. These add lots of little features to the terminal (a buffer to scroll back, split terminals, persistence so you can detach and reattach) (tmux is more modern feeling, IMO).
Assuming you tried moving the cursor vertically, have you tried the alternative approach of Store Cursor Position / Restore Cursor Position cf https://stackoverflow.com/questions/28986776/ansi-escape-seq...
The scrollback buffer may be a limitation, so you should try with enabling or disabling the alternate screen (ti/te)
If that fails, you may have to tweak your terminal emulator to "hook" the SCP/RCP to a specific point of the scrollback buffer, to allow this scrollback.
You'd be better off piping into less / more / most. These are called "pagers" and are designed to do this. eg
cat large-file | grep common-phrase | less -F or --quit-if-one-screen
Causes less to automatically exit if the entire file can be displayed on the
first screen.
(Also handy: add in `-X` to leave the contents on the screen when you exit less)