My ramblings and thoughts.
I recall hearing that Jeremy Crawford said that sometimes invisible creatures will be hidden without making Stealth (Dexterity) checks. Even if he did not say this, it seems the logical way to run it to me, with the DM deciding when these circumstances apply.
Detecting invisible creatures sometimes reminds me of invisible characters in movies and TV shows. To give the audience an idea of where they are, they make noise, disturb plants or curtains, bump into things, knock things over, pick things up (that remain visible), leave footprints, etc. Clearly they are not taking an action to hide! Invisible creatures moving in crowded/cluttered areas will need to make Dexterity (Stealth) checks or they will bumble through, revealing their location and direction of travel.
There will be times when there is not much (or nothing) in the environment to bump into or disturb, or there may be other circumstances or distractions that help cover signs of the invisible creature's presence or passage (loud noise, smoke, environmental hazards, darkness, other (visible) opponents, terrain features, etc.). In those cases, I might rule the creature to be hidden. Additionally, depending on the situation, someone (unaided) might have a harder time determining an invisible creature's location and/or direction of travel. I would reflect this in various ways, from Wisdom (Perception) checks at disadvantage, to indicating larger areas with a successful Wisdom (Perception) check (instead of indicating a single square, I would indicate 9, 16, 25, etc., squares, up to more general zones (for example, "You think your unseen assailant is somewhere north of you."), up to declaring the invisible creature cannot be perceived without additional aid, usually magical, or until circumstances change.
Some rules references (emphasis mine in the quotes).
D&D 5th Edition Player's Handbook p.291 said:
Invisible
• An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured. The creature's location can be detected by any noise it makes or any tracks it leaves.
• Attack rolls against the creature have disadvantage, and the creature's attack rolls have advantage.
Invisible references heavily obscured, so we go to:
D&D 5th Edition Player's Handbook p.183 said:
A heavily obscured area -- such as darkness, opaque fog, or dense foliage -- blocks vision entirely. A creature effectively suffers from the blinded condition when trying to see something in that area.
Not much added here. Heavily obscured refers to Blinded, so we go to:
D&D 5th Edition Player's Handbook p.290 said:
• A blinded creature can't see and automatically fails any ability check that requires sight.
• Attack rolls against the creature have advantage, and the creature's attack rolls have disadvantage.
So why lead us to Blinded? The second bullet (advantage/disadvantage) is already in the description for Invisible, so the first bullet must be relevant to Invisible, which leads me to believe that you cannot "see" a hidden invisible creature. You may see signs (moving grass, a knocked over vase, a blood trail), or you may hear them, but you cannot detect
them visually. RAW, invisibility is not like a super duper
blur, or the Predator's invisibility where if you pay attention you can make out their form. DMs are free to rule otherwise in their games, of course.
For those who insist you always have to take an action to hide, I have this oblique inference:
D&D 5th Edition Dungeon Master's Guide p.232 said:
Boon of the Night Spirit
While completely in an area of dim light or darkness, you can become invisible as an action. You remain invisible until you take an action or a reaction.
If you always have to take an action to hide, it would be impossible to hide with this, though it seems like it should be something one could do with an Epic Boon, otherwise, it ain't all that Epic.