'a little bit earlier' is a correct and usable phrase in written English. It is typically used to describe a time that has passed before a certain point in time, or a situation that has occurred before something else. Example: "I arrived at the party a little bit earlier than expected.".

The phrase "a little earlier" is correct and usable in written English. You can use it when you're referring to a specific time that is before the present time. For example: "I should have left a little earlier, so I would have avoided rush hour traffic." He did it in 1918, a little earlier than Post.

"a bit sooner" is a correct and usable phrase in written English. You can use it to indicate that you would like something to be done more quickly, or at an earlier time than expected. For example, "I'd like to have the report finished a bit sooner this time, so let's aim for a deadline of Friday."

"Early" would refer to the first period (first days, weeks, months, even years) that the club was in operation. "Earlier" would just refer to a time before the other time period being discussed ("last years"), but not necessarily the first period that the club was in operation.