How can I rush base upgrade without having farm accounts?

Base upgrades require resources which you will need to produce or raid in game, or pay for as benefits / packages with real money. If you are able to spend a lot of time on the game then attacking other players /zombies for resources can be quicker than farming but is likely to make you enemies. Gathering is fairly slow but works well if you are not able to spend a lot of time in game.

Having farms will mean some set up work but lets you have a set of safe targets and a steady income. It will still not be really fast though. The game is not designed to let you max your self in a few weeks or even months. The game would be too easy then.

The only short cut is to buy packages and other benefits with money although it will still take a lot of purchases to make a large difference.