Upgrading the site is the third question, not the first. Two things have to be true before any on-page work can produce a visit, and both are checkable in an afternoon.
First, is the site actually in the index. Optimising a page changes nothing while the search engine isn't holding it, and being live isn't the same as being included. Search your exact domain and look for your own pages; if they aren't there, the work in front of you is inclusion, not content.
Second, does anyone search the words you optimised for. This is where most one-month reports come from. If the terms have no volume, the page can be perfect and still get nothing, and no amount of upgrading changes that. If they do have volume, look at who currently fills the first page. A month-old site rarely outranks established pages, which means what you're seeing isn't a fault, it's the normal starting position.
Those two answers point in opposite directions, so it's worth knowing which one you have before you touch the site again.
Best,
Floqal