It's never too soon to introduce testing and the sooner you do it the sooner you will start finding the bugs.
I'd start with testing from two different view points. Firstly if you have some fairly standalone java classes being used for things like business logic and data processing, I'd start create JUnit tests for them ti winkle out internal code issues.
Secondly I'd be looking to create tests for the use cases specified by the business. These would most likely be done in something like Selenium because you want the test to follow the interactions with the web site as specified by the use cases. Leave the nitty gritty to the JUnit tests behind the scenes. These are the high level confirmations of functionality.
All of this will take time and it's unlikely that management will allow you to do nothing but testing for a couple or weeks or more. Instead the mostly likely way to handle it is to do it as you go. Pad out your time quotes for fixes and new features to allow for writing the tests. Remember that writing tests can take 50% or more of the time, especially when you are starting to fill them out. The time will back off a bit once you have a wide range of suites, but even then some tests are harder to write than the code. But they are worth it.