The rules expect the DM to decide on a case-by-case basis
First and foremost, there are no skill checks in 5e anymore. Things like "Wisdom (Insight) check" are ability checks, and they differ from skill checks as they were in previous editions.
Moreover, "passive check" is a game term which has a special meaning in 5e:
A passive check is a special kind of ability check that doesn't involve any die rolls
What you're asking about is probably a regular ability check made by a DM's call, not a passive check. Keeping in mind that all ability checks are made by a DM's call, the real question is: does the DM have to wait for a specific question from a player before asking for an ability check?
And the answer is — no, the DM does not have to wait for a specific question. The 5e ruleset is a toolbox the DM is free to use at their own discretion. It does not set any hard limits on the DM anymore, especially when we're talking about ability checks.
It was the 3.x thing to explicitly frame the process. 5e left the prescriptive paradigm regarding ability checks. Now the game expects the DM to decide, what checks would be better for the story. This is also known as the "rulings over rules" principle.
So it's up to the DM if she thinks it'd be better to wait for a specific question before asking for an ability check in each case. What I want to suggest is two things: avoid no-brainers and don't expect specific "right words" from the players.
If players get a chance to learn additional information only when they say "I want to listen/look closer", they will be saying this every time, getting zero results most of the time. It is a no-brainer and no-brainers are bad design — they waste real time and make games less exciting. Instead, assume the characters are always aware and asks for a check only when the outcome is uncertain.
Don't expect specific "right words"
Don't expect the players to do only specific things you had in mind when you was preparing the adventure. This is also true regarding puzzles. If you allow a dice roll only if the player says "I want to check if it's an imitation", they probably never get any dice rolls. Instead, treat any examination effort as a potential revealing of an imitation.
Know your players
DMG p.236 allows a playstyle when players do not roll dice at all (unless it's a combat, but combat is a different story). Some players just like rolling dice and enjoy randomness, some prefer more predictable approach. The DM's job is to decide what would be better for the table. The DM can still use passive score for the information PCs are able to get intrinsically and/or ask for a check. Both options are "correct" from the rules perspective.
Putting this in a nutshell:
- assume proactivity and competence of the players' characters
- allow broad interpretation of what is the right thing to do for moving the story forward
- don't hide information if it is important for the story
How would this work in-game:
— You can definitely hear a sound from this cave. It's like a baby crying.
— That's creepy! I draw my sword. Can I say if it's a human baby?
— Make a Wisdom (Insight) check.
— Suddenly you realize it's not a baby. It is an imitation, quite crude, actually. Like some kind of non-human creature is trying to mimic a toddler's babbling.
— You can definitely hear a sound from this cave. It's like a baby crying. (checking the PCs Wisdom (Insight) passive score) You insight allows you to understand it is an imitation, like some kind of non-human creature is trying to mimic a toddler's babbling.