Can I create a Hyperlink/Button that reads its cell reference from another cell?

Welcome to the forum.

You need to put a hash sign in front of the column range.

Option 1.
Put #G:G in A1 then use this:

Formula:

=HYPERLINK(A1)

Option 2.
Leave just G:G in A1 and add the # in the formula:

Formula:

=HYPERLINK("#"&A1)

Option 3.
Just put the column letter in A1 and use this:

Formula:

=HYPERLINK("#"&A1&":"&A1)

Friendly Name
Personally I'd add a 'friendly name' for the hyperlink as well, using something like this:
For options 1 or 2:

Formula:

=HYPERLINK("#"&A1,"Col "&LEFT(A1,FIND(":",A1)-1))

For option 3:

Formula:

=HYPERLINK("#"&A1&":"&A1,"Col "&A1)

Hope that does what you want.