Space can be somewhat inferred by cells through hormone and signaling molecule gradients. So if a central group of cells can start releasing some sort of signaling molecule, and as cells get more distant from that central packet of cells they get less of that molecule, changing their behavior (ie gene expression).

Cells can also divide non-symmetrically, where one cell stays as one type and the other differentiates into a new cell type, creating shape. Cells can pass on information on what genes to express through chemical marks left on the DNA (and the proteins bound to the DNA) telling the new cell what genes to express and what genes to repress.

In the end, though everything does come back to gene expression, which is regulated by a complex network of gene expression networks generated by where the cell originated and what signals it is getting from where it is in the organism.

Interesting the actual genome in the nucleus does have a conserved 3D shape, which has a big impact on how it regulates its genome.