Ability to load init script in Firefox?

I have a long time stick with Conkeror as my default web browser and get used to configuring/adding new features to my browser using js code with all the XUL Api through the .conkerorrc file. I'm migrating to Firefox since it has better support and is actively maintained by Mozilla. However, one of the feature that I've been missing so much is the dot file, which I can easily configure anything that I like, back up all of them through git and eval the code directly (using Mozrepl) while I'm coding to see the result.

Is there any way that I can inject/execute a sciprt on Firefox startup, for example ~/.firefox/index.js?

There is no functionality in stock Firefox to execute JavaScript code supplied by the user at startup. Functionality like this has been something that has been requested of Firefox since 2006-04-02.

It is trivial to write an add-on in any of the different Firefox add-on types (XUL/Overlay, Restartless/Bootstrap, Add-on SDK, or WebExtensions) which would run whatever JavaScript you desire upon Firefox startup. This could be done to either run code that was included in the add-on (simple), or that runs the JavaScript contained in a file that is loaded from a location external to the add-on (more complex). Which add-on type you used to implemented this would impact which interfaces you had available within the code you write. One drawback of writing your own extension which runs code included in the add-on is that in order to use it with a release, or beta version of Firefox is that you would need to have it signed by Mozilla. While this is a quick and easy process, it does add some additional overhead to the development/test cycle.

You have not specified any of the firefox-addon tags in your question. In addition, you have not described the functionality you desire, except as generalities. It also does not appear to be the intent of your question to ask how you would implement such an add-on. Given those and the fact that there are already multiple add-ons that implement the functionality of running arbitrary JavaScript (including XUL) code supplied by the user, I am not going to supply code here which performs this function.

However, if you are interested in using an already existing add-on, here are a few options:

• userChromeJS: This extension was derived from the code originally provided as an example of how to implement the functionality requested in bug 332529. Its first feature listed is: "Complete chrome customization is possible by running custom javascript code or overlaying chrome with .xul overlays." This is an Overlay based add-on with which you can use XUL. This sounds like the functionality what you are interested in obtaining.
• uc: "A userChromeJS clone with built-in subscript/overlay loader capability."
• Greasemonkey: "Customize the way a web page displays or behaves, by using small bits of JavaScript." This is a commonly used add-on which permits writing more complex JavaScript code. The code is executed in a sandbox, not in the scope of an extension. This is done for security reasons.
• Custom Style Script (Inject desired CSS or JS): "Add Custom JavaScript Codes or Styles (CSS) to an specific page or all pages."