Hi,
For sure you can, but I - as a professional designer - would never do.
Why make things harder than necessary?
--> Just use a dedicated boost converter (IC). It comes with datasheet, schematic, useful features, detailed explanations, and you can be sure it works like expected.
If you do it with 555 you don't get all the benefits above. It's more likely to fail.
If you want more detailed informations, then you first need to give more informations: At least:
* input voltage range
* output voltage
* output current
* everything else that may be important for you (cost, size, efficiency, availability, part count, features like current limiter...)
Klaus