You can't set text frames to dynamically move based upon their contents. More specifically, you can't control the origin point of the text frame dynamically. You can set text frames to grow based on content, but not simply move X cm.
However... This isn't very elegant and I wish there were a better method but you may be able to utilize an additional return and a Paragraph Style to create the visual space at the top of the page.
Let's say you want 5cm at the top of a page following a hard page break. All you need do is set up a paragraph style with the Space After set to 5cm. Then set the "next style" option back to the original paragraph style.
Insert the hard page break, add a line feed and set the paragraph style. Basically, the key strokes would be - Enter, Return,
You need an extra line feed there so that the space after is implemented. You can't set a space before at the top of a text frame. Space Before is ignored at the top of a frame. The extra line feed + space after will work though.
While this doesn't move the text frame, it will add the space at the top of the next page resulting in the same visual alteration.
As LaurenIpsum points out in the comments above, you could utilize master pages with text frames. But the master page would need to be applied to the page following the forced page break.