I wouldn't really suggest it unless you know what you are doing. and that is to root your phone and install a custom rom. You can find everything you need on XDA forum and although some methods may seem simple, you always stand the risk of bricking you phone, rendered useless and unrepairable. This is the only alternate option I can think of.
Not by any official means as the Note 10's firmware ended at Android 12 as Carlvig has stated you could go down the custom ROM route but that'd mean running uncertified software and could open device up to vulnerabilities and unsupported apps