Can I check the notice of authorization for the progress of utility model patent application?

There's no need to ask. After applying for a patent, the relevant departments will notify the applicant in writing at every step, so don't worry about missing the necessary procedures.

After admission, you will be informed to pay the examination fee first, and then start the examination procedure. Invention patents need to be published after preliminary examination. After publication, the substantive examination procedure will begin at the request of the applicant. If there is no reason for rejecting the substantive examination, a notice of granting the patent right shall be issued, and after paying the necessary fees, an authorization announcement shall be issued and a patent certificate shall be issued.