Here's what we do know:
* The earliest known collection of his poems, "Venus and Adonis" and "The Rape of Lucrece", were published in 1593 and 1594 respectively. However, these works likely circulated in manuscript form before that, meaning they could have been written earlier.
* Shakespeare's sonnets, published as "Shakespeare's Sonnets" in 1609, were written over an extended period, meaning some could predate the works mentioned above.
* He also wrote poems for different events and occasions, some of which were likely printed at the time.
In conclusion, we don't have a definitive answer to your question, and the search for Shakespeare's first published poem continues to be a fascinating puzzle for literary historians.