In this question we see that two-weapon fighting with darts is not possible because they are not melee weapons. Let's replace the darts in that scenario with daggers, which are valid light melee weapons for two-weapon fighting, and also have the thrown property.
Two-weapon fighting says:
When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative.
If either weapon has the thrown property, you can throw the weapon, instead of making a melee attack with it.
Consider this scenario:
Bob the rogue has two daggers drawn and ready to go. He throws his first dagger as his attack action, satisfying the condition of "when you take the Attack action and attack with a light melee weapon that you’re holding in one hand."
At this point, he is no longer holding this weapon in hand because he has thrown it. He is now holding only one dagger, in his other hand. In this case, the condition above has been met, but does he get to use the bonus action to attack with a "different light melee weapon [held in his] other hand" even though he is now wielding only a single weapon?
In other words, is the bonus attack granted at the moment the first attack made, as long as you meet that first condition of "attack[ing] with a light melee weapon that you’re holding in one hand," regardless of how many weapons you end up holding after the first attack?