: How to copy/replicate files w/o changing the access time

[Greaser, Tom]

Have you tried  cp -p 
      --preserve[=ATTR_LIST]
preserve  the  specified attributes (default: mode,ownership,timestamps), if possible additional attributes: context, links, xattr, all

or tar  --atime-preserve[=METHOD]
preserve  access  times  on  dumped files, either by restoring the times after reading (METHOD='replace'; default) or by not
setting the times in the first place (METHOD='system')