No. An act is only selfish if it is possible to have chosen to do something else (e.g. it is not selfish for you to return to earth after jumping, even if you intend and receive some benefit from it). If there is no choice, no alternative, no other option in the matter, then an act cannot be selfish. Now, if every choice, every decision, that we make and its associated act, is tainted by selfishness at its root, then it is impossible for us to choose otherwise, since the act of choosing is itself always a selfish act. However, in this case it is impossible to not be selfish, and there is no choice, no alternative, and no other option. Therefore, there are no selfish choices.
Evidently, this is a contradiction. Either, you can reject the premise that an act is only selfish if it is chosen, or reject the premise which associates every possible choice with selfishness (i.e. adopt a different definition of "selfish"). I prefer the latter.
(Edit: technically, it is not the impossibility of an act which is relevent, but whether an agent thinks that an act is impossible. For example, if you thought that it was possible to defy gravity, then falling to earth might be a selfish act, even though, objectively, the act was not possible. In consequence, an agent can be selfish even if it were impossible to be selfless, objectively, because they might think they were choosing among alternatives. However, if you think that every choice is selfish, then you fall back into the aforementioned paradox. In other words, a selfish choice is contingent not on the truth, but what an agent thinks is true, even if they are wrong.
In consequence, it cannot be true that every choice is selfish if selfishness must be a choice, because if we hold the view that every choice is selfish, then there is no choice but to be selfish, and thus no selfish choices. Objectively i.e. the universe does not contradict itself.)