QUOTE: “We do use it for ranking, but it’s not the most critical part of a page. So it’s not worthwhile filling it with keywords to hope that it works that way. In general, we try to recognise when a title tag is stuffed with keywords because that’s also a bad user experience for users in the search results. If they’re looking to understand what these pages are about and they just see a jumble of keywords, then that doesn’t really help.” John Mueller, Google 2016
Length of site domain registration; (I don’t see much benefit ON IT”S OWN even knowing “Valuable (legitimate) domains are often paid for several years in advance, while doorway (illegitimate) domains rarely are used for more than a year.”) – paying for a domain in advance just tells others you don’t want anyone else using this domain name, it is not much of an indication that you’re going to do something Google cares about).
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.