Most small businesses owners and marketers know a little something about SEO (search engine optimization) and the different tactics to help your website rank well in organic search engine results. Another important tactic for any Internet business to know about is SEM (search engine marketing), which includes things such as search engine optimization, paid listings and other search engine related services.
A poor 404 page and user interaction with it, can only lead to a ‘poor user experience’ signal at Google’s end, for a number of reasons. I will highlight a poor 404 page in my audits and actually programmatically look for signs of this issue when I scan a site. I don’t know if Google looks at your site that way to rate it e.g. algorithmically determines if you have a good 404 page – or if it is a UX factor, something to be taken into consideration further down the line – or purely to get you thinking about 404 pages (in general) to help prevent Google wasting resources indexing crud pages and presenting poor results to searchers. I think rather that any rating would be a second order scoring including data from user activity on the SERPs – stuff we as SEO can’t see.
Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.