You have several options:
Make the form a Single Page Application; ie, have all the steps of the forms on a single page (like tabs). Basically, it is all just one form which will only get submitted at the end.
Store the intermediate form results on the browser's localStorage. Check if there is something in the localStorage and pre-fill the form. The complete response is only sent to the server at the end.
Store the intermediate form results in the server. This means that after each step the partial response is stored and the next steps builds up from this. You can do this if the next step heavily depends on the previous step and you cannot make it a Single Page Application (SPA).
For options 1 and 2, you can dynamically pre-fill form inputs using javascript, for option 3, the form inputs will come pre-filled from the server.