They don't change significantly..
..unless you count (apparent) size (more on that on SciFi SE).
"Clearly, the pitiful humans at Hasbro are so overwhelmed by the
awesomeness of Cybertronian life forms that they can't get the scale
- Starscream breaking the fourth wall in Transformers Comic Issue 23
The 'life cycle' of Transformers does nonetheless have a sequence of stages that can be interpreted as 'growing up':
"Transformer life begins with the purposeful construction of a body by an existing individual or group". At this stage, the 'protoform' (introduced in the Transformers spin-off Beast Wars), "an unfinished, "embryonic" Transformer body", is the first identifiable stage, which can be seen as birth, since "these simple "skeletal forms" [..] are kept covered in nutrient gel within stasis pods that nurture and protect their apparently fragile forms".
Alternatively, the Transformers have been created directly as "complete, fully mechanically built and functional, though lifeless, robotic bodies".
From spark to protoform.
at a certain point, these newly constructed forms are either "switched
on", infused with life from an outside source, or
scan an alternate form, and solidify into a finished, mechanical
robotic form. Life begins.
They are "preprogrammed with a complete personality and most of the basic knowledge necessary to survive and socialize in the world". I gather they have self-learning abilities, and at this point there enters a stage with relatively no changing or ageing, except in their programming. They can live for "millions of years without any noticeable alteration or ageing", and are theoretically immortal. Some individuals seem to have an altering appearance, and are
shown to look different and "younger" at earlier times in their lives.
These changes seem to be signs of advancing age. While they could also
be a simple factor of their gaining new or upgraded bodies, the clear
intention is that their later forms are more lined, worn and less
spry, suggesting ageing.
Jetfire in Transformers: Revenge of the Fallen. A robot. With a cane.