You can relatively easily achieve this.
On the form editor navigate to Form Elements panel and find Structure accordion. There you have “Page” element. Drag-and-drop 2 pages to your form. So the first page is going to be your form with submit button, and the second one will display our thank you message.
Add submit button to the first page and don’t forget to specify submit actions (don’t add a redirect in submit actions). Select "Next" for the Navigation step field.
Add “Text” component to the second page and write a thank you message.
Navigate to the Settings tab and set “AJAX enabled” checkbox. Save the form.
Now when you click on the submit button, you’ll see thank you message.
Please don’t forget that you need to have Sitecore 9 Forms scripts and styles loaded on your page.
You can do it with:
@Html.RenderFormStyles() //inside head tag
@Html.RenderFormScripts() //before closing body tag.
Idea and code taken from: http://www.apiqu.com/blog/2018/August/sitecore-9-forms-thank-you-message