The short answer is maybe early June around here, but prime crop will be July though the long answer is:
This is a hard one to answer as it depends on a number of factors. In general around here I can tell you that garden centers, etc. typically have small tomato plants for sale around March 1st, and depending on the variety of Tomato you are looking at 60-80 days before the first tomatoes are ready to pick. The catch is many years there will be a late season freeze that may kill unprotected tomatoes as late as the first of April, though there was no such freeze this year. This is true of where I live about 80 miles inland in western Louisiana. In southeastern Louisiana closer to the coast the chance of such a spring freeze is MUCH lower, and I suspect in some parts of coastal Louisiana tomatoes may be planted as early as February. The issue is that Tomatoes really need warm weather to really start growing fast, this time of year you may see highs in the 80's one week and 60's the next.