Has it always loaded slowly? Is this a CMS or WordPress site? You should look into setting up caching. Also if you can make it into a static site would improve load speeds. Database optimization, gzip/brotli, etc.
Otherwise, yes, hosting quality will matter. An overloaded shared hosting server will do that, so getting quality hosting that is on performant servers and network is pivotal, but also the hosting company matters because more often than not, you are left guessing why your site is load slow or not at all while you are reaching limits on the plan resources. For example, our Optimal Web Hosting accounts you know what you get for resources like a VPS, it's transparent on the plan you choose (unlike unlimited everything plans, which is actually never unlimited anything, that's the reality, and 'unlimited' server resources is a marketing bait switch you to higher plans or VPS)
