It's an interesting question, but I think the question itself is flawed for a few reasons. The answer is something like "it never did." Even today, with recordings and commercial jingles often being made for money, most music in the world is not made "explicitly for the purpose of profit." If you want to be rich, you don't pursue music. This is a pretty hot topic of discussion among professional musicians, many of whom feel that after 20 years of training they should be paid more, and that it is not fair that because they are "pursuing their passion," they are expected to be content with the privilege of making art for a living in lieu of typical benefits and typical levels of financial security. (or that people sometimes suggest that be paid in beer/food/"exposure.")

But anyway, music and money have been linked (and not linked) for a very long time. On one hand, it seems that money and/or resources have always changed hands for music. On the other, people have always made music anyway, even when they're not getting paid, and music has long been available for "general consumption" -- we can't say for sure exactly what happened at all times, but before recording existed, there is lots of evidence for music happening at bars, impromptu dance parties, in-home sing-a-thons, parties, festivals, and parades.

In early modern Europe, lots of aristocrats paid big money for music. They often hired the best musicians for their courts and church services, and sometimes even used musicians as the subject of foreign negotiation ("I'll lend you my best soprano for a few months if....") or to impress visiting diplomats. You can imagine the sycophantic themes of some of these performances, which arguably hit their highest level of flattery in the French court of Louis XIV.

And in earlier medieval Europe musicians were also employed under aristocrats and religious elites, working at courts or at prestigious universities/religious institutions. Music of pre-medieval times is not my specialty, but maybe someone else can comment on financial-musical transactions during more ancient days.

So, at least in my awareness, music has always earned money. But you wrote "as opposed to something people did because they were passionate" -- and this is a false dichotomy. Although music was considered a technical craft or even a science at different points in history, the idea of it being related to emotion appears constant.

Outside of professional music circles, and within them, passion or heart seems to have always played some role. Trained or not, paid or not, people have made music throughout history. Humans make music, just as they tell stories, have sex, dance, chit-chat, and eat together.

Primary sources from all the eras I can think of tell about the physics, theory, and techniques of music--but also write of the magic of music, of hearts being moved and minds being changed. The words "cantare," "chanson," and "chant" share etymological roots with the words "incantation" and "enchant." To sing a song is to cast a magic spell. As far as we can trace, this has always been part of humanity.