Parseltongue is considered an 'inherited magical ability', meaning it is passed down through the bloodline. Does this mean that you are able to speak Parseltongue when you are a 1 month old baby (creepy baby)? Or does the ability to speak to snakes come around the time that you learn to speak a human language?
It’s not really clear from the information we have.
There’s no example of a very young child just learning to speak English speaking Parseltongue - everyone we see speaking it is already old enough to have already learned English.
Harry (although his ability to speak Parseltongue was not truly his) was able to speak Parseltongue by the age of ten.
“As the snake slid swiftly past him, Harry could have sworn a low, hissing voice said, ‘Brazil, here I come … Thanksss, amigo.”
- Harry Potter and the Philosopher's Stone, Chapter 2 (The Vanishing Glass)
Tom Riddle also learned he could speak Parseltongue before he attended Hogwarts, but the actual age he found out he could speak it isn’t clear - though it would be before 11.
“Riddle nodded. Dumbledore got to his feet and held out his hand again. Taking it, Riddle said, ‘I can speak to snakes. I found out when we’ve been to the country on trips – they find me, they whisper to me. Is that normal for a wizard?’
Harry could tell that he had withheld mention of this strangest power until that moment, determined to impress.”
- Harry Potter and the Half-Blood Prince, Chapter 13 (The Secret Riddle)
The Gaunt family (Marvolo, Morfin, and Merope) spoke Parseltongue to each other at home as a sort of second language even when not talking to a snake, though it’s unclear at what age any of them learned it. It’s possible they became capable of speaking both languages at the same time - but it’s also possible that they learned one first, then the other.
““Darling”,’ whispered Morfin in Parseltongue, looking at his sister. ‘“Darling”, he called her. So he wouldn’t have you anyway.’ Merope was so white Harry felt sure she was going to faint.
‘What’s that?’ said Gaunt sharply, also in Parseltongue, looking from his son to his daughter. ‘What did you say, Morfin?”
- Harry Potter and the Half-Blood Prince, Chapter 10 (The House of Gaunt)
The Gaunts do seem to prefer speaking Parseltongue over English, most likely as a way of keeping what they’re saying hidden from others, and because it’s a mark of their heritage whereas English can be spoken by anyone.
Since it was an innate skill, it’d be easier to learn than English.
When children first start to talk, they have to learn individual words and their meanings. However, Parseltongue (at least for those who have the innate ability to speak it - rather than learning it like Dumbledore did) seems to be something that is picked up all at once. While Harry is a special case since it’s not his ability, young Tom Riddle also didn’t seem to need to learn individual words to be able to speak Parseltongue, it sounds like he knew it all at once.
However, it may or may not still need a knowledge of a human language first - this is unclear from the information we have.
Phillipus Aureolus Theophrastus Bombastus von Hohenheim (Paracelsus) is known for the discovery of Parseltongue in 16th Century. Mentioned in Harry Potter and the Philosopher's Stone, Chocolate Frog Cards (here).
Apart form Harry, the most well-known Parselmouth was Salazar Slytherin himself. Then came Voldemort and even Dumbledore. According to Pottermore here,
As J.K Rowling revealed, Albus Dumbledore had mastered Parseltongue too. – although he could not speak it aloud. We’re not sure why Albus learnt the language, but perhaps the Hogwarts headmaster wanted a better understanding of Voldemort.
Lesser known Parselmouths were the Gaunts (Voldemort's Uncle, Grandfather and mother). As seen in one of the memories in the Pensieve in The Half Blood Prince, Morfin and Marvolo Gaunt always conversed in Parseltongue (their English shows that they learnt it very late; English was probably their second language). As Rowling puts it,
Seeing as the Gaunts were so dedicated to their pure-blood line, it makes sense they would isolate others as much as possible by using their own language.
So indeed being a Parseltongue is quite rare, but it can be learnt as any other language (Dumbledore proved it! Yay!). But the important thing is that Parseltongue usually requires the speaker to face a snake-based creature or object shaped like a snake. However skilled parselmouths like the Gaunts were able to speak at will.
In conclusion, One can speak Parseltongue at any given age. Parseltongue may even be the first language you learn. Very little is known about the Gaunts but, by looking at their fluency, it could be possible that they learnt Parseltongue first and then English.