How many NHL players scored their first career goal on an empty net?

This is a question that defies a definitive answer, since the available long-term statistics do not break out empty net goals from other scoring.

There is one group of players where this has been tracked, and that is for goaltenders who have been credited with goals. Many goalies have tried to shoot the length of the ice into the opposing team's empty net, but only a few have succeeded. A few others have benefited from the credit for an own goal in the NHL being given to the last *opposing* player to touch the puck. Since it is so rare for a goaltender to get any scoring points of their own, it is very likely that their first goal will be an empty-netter.

Eleven goaltenders have scored a total of fourteen goals in National Hockey League (NHL) games... ...All NHL goaltenders who have scored a goal by shooting the puck have done so with an empty net; the goals credited to goaltenders that did not shoot the puck were all the result of own goals by the opposing team who had their crease vacated.

https://en.wikipedia.org/wiki/List_of_goaltenders_who_have_scored_a_goal_in_an_NHL_game

There are almost certainly other players whose first NHL goal was into an empty net, but the statistical sources to find them just don't exist.