I've read somewhere that it wasn't until the last half of the 19th century that orchestras started to be composed of professional musicians - but I can't find the source. I could imagine that emperors and kings would have had professional musicians at their courts, but a whole orchestra?
The problem here is when you want to call an ensemble an orchestra. Professional musicians and professional composers certainly were employed in ensembles at courts, and in the households of the wealthy and noble. They were essentially servants in the household, and the household would often own the instruments. Judging from the 1542 inventory of musical instruments of Henry VIII, clearly there were some large ensembles at his court, but it would not have been limited to England. Ensembles of musicians employed in courts continued through the Baroque and Classical periods, when ensembles could certainly be called orchestras. Monteverdi, Handel, Bach, and Hayden were each a Kapellmeister or maestro di cappella in charge of writing music for their patrons or for a church, and rehearsing and conducting the musicians. And they were still servants: wherever the patron went, the musicians could be hauled along. When Nikolaus I, Prince Esterhazy stayed much longer than usual at his summer residence in Hungary, the homesick musicians begged Hayden to ask the prince to return to Austria so they could see their families, and Hayden wrote his Farewell Symphony as a way to politely request the prince to do that. When Handel wanted to go to England, he had to ask his patron George Elector of Hanover for permission. He was told he could go but had to come back: but he didn't. Which was embarrassing, when George became King of England, and Handel had to engineer a reconciliation with his new monarch.
There would also be large ensembles needed for opera, and some of those are early, like the Teatro Goldoni in Venice, started in 1621, and the Oper am Gänsemarkt in Hamburg, in 1678.
But certainly the late 18th and early 19th c. saw greater urban populations, industrial economies, and , with those, the appearance of professional composers that tried to do without patrons, like Mozart and Beethoven, and concert halls that could sell tickets for large orchestral concerts. But you could say that it was after 1840 or so that the orchestra became the big ensemble that you expect now, filled with brass, woodwinds, percussion, a harp, strings, etc. , and the instruments within it also became louder, in order to play for those very big audiences in very big halls..