With Adobe Illustrator, creating vector content, there is no PPI to be concerned with. Vector graphic are resolution independent and don't adhere to any specific PPI.
So, you merely create a document with an artboard which is 7500x7500px and then create your artwork on that artboard.
If you are placing raster images into this Illustrator document, you will want to ensure all raster images are at 300ppi before you place them into the Illustrator document. And then do NOT enlarge placed raster images within Illustrator. Enlarging raster images within Illustrator will lower the image PPI.
If you intend to use the built-in effects withinin Illustrator such as drop shadows, blurs, and glows, you will want to adjust the Document Raster Effects Settings in the Effects Menu.
Resolution drop down to "High" and the ppi field should then read "300".
Note that this only alteres raster items created within Illustrator this setting does not alter any placed raster images.
CS6 screenshots, but it's all the same in CC, windows may look slightly different that's all.