An increased time to 1st byte means your website is running too many SQL queries or non-optimized SQL queries which can also include server-side calls to third-party APIs.
If you’re a WordPress user, there are a number of plugins you can check out to decrease the number of database queries and speed up your website. And if you are not using WordPress then you need to check and optimize your database then use some website cache functionality. For this, you may buy expert’s support via firstname.lastname@example.org on per hour per terminal basis.
You should also know that caching plugins affect the performance of any website both positively and negatively and it’s largely dependent upon the traffic, and how dynamic your website is.
For instance, WP Super Cache works well on most shared hosting plans whereas W3 Total Cache is useful on servers or VPS with more resources available. Popular choices for WordPress cache plugins are WP Super Cache, W3 Total Cache, Batcache and Tribe Object Cache. These plugins offer various page, database and browser cache features. Try each one out (one at a time, not all at once) to see what works best for you.
Other things you can do for optimizing database and reducing the number of queries generated on your website is clean up your database – remove old transients and remove garbage and data left from old deactivated plugins – try plugin garbage collector.