Working on a website, I use Google Tag Manager and push some info with the dataLayer in Javascript. So far so good. However there are some information that should not be see
In 2020 Google has released Google Tag Manager for server-side tracking, where you run a container in a cloud environment that then distributes the requests. https://developers.google.com/tag-manager/serverside
Facebook and Google Analytics Support this now. So you can move tracking to server side.
GTM for the Web is basically a Javascript injector - the Interface is there to configure your tags, then everything is wrapped into a JavaScript function that is inserted into your page and executed by the browser. There is no serverside component that you could push data to.
So quite probably the answer is no (unless you want to try really weird workarounds like running the container in a headless browser on your server or trying to abuse the mobile SDKs for GTM, which works rather differently than the web version). I guess it would be easier to send your serverside calls directly to the respective tracking services.