Is it Possible? Yes, with enough time and effort anything is possible. Is it a good idea? No, you should port your application to Mendix.
Mendix is a full-stack platform which offers development using an abstraction over code, it is not a cloud platform that you can use to deploy any web-app.
You could port your existing code into Mendix components in the form of JavaScript actions and Pluggable widgets. This would allow you to later on refactor your code into Mendix flows and pages.
Take a look at the documentation for JavaScript actions and Pluggable widgets to get an idea of what your options are:
https://docs.mendix.com/refguide/javascript-actions
https://docs.mendix.com/apidocs-mxsdk/apidocs/pluggable-widgets