It would seem that way RAW, but I've always allowed players to cast and use it in the same action. This seems rules as intended but poorly worded maybe? Then again Ive never given a whole lot of thought and just figured thats how it worked. Is that how it worked in previous editions, ICR?
I concur with no by RAW. Furthermore, it's a cantrip. Let's not be too generous with it's usefulness and utility. Man oh man, but cantrips are a whole different animal now than they were back when they were first introduced in 1E/2E.
Of course, it's a non-concentration cantrip with a 1-minute duration. So if you're in a dangerous area and not trying to be stealthy (i.e., you've got some heavily armored folks along), you might as well keep a mage hand up at all times.
The arcane trickster has a more powerful mage hand it can use. It has a few cool powers that say the mage can use its bonus action to control the hand for things like pick pockets and open locks, as well as distracting bad guys for advantage. So it would seem that you cannot unless you are an AT.
In my game I would likely let you for general things like cast it and have it carry a torch or pick up something off a table. Maybe not combat related, not sure.
It costs an action to cast and it costs an action to control so absolutely not. Unless Arcane Trickster - then yes because controlling it, for you, is a bonus action.
I suppose an Eldritch Knight could also do it at the cost of an action surge, but that seems a bit steep except for exceptional circumstances. I'd probably allow an EK to cast and then control the hand with a bonus action, as part of War Magic - but that's clearly not RAW.
Given that it is primarily a non-combat cantrip, two actions being necessary to cast and subsequently operate mage hand is not at all unreasonable. And, in most non-combat cases, irrelevant that it takes 12 seconds vs 6 seconds to actually do something with it.
I use it in combat with an Arcane Trickster all the time, usually as a bonus action.
Dumping a flask of oil before you attack with Green Flame blade, pouring holy water, using caltrops, ball bearings, hunting traps and most of all stealing things like an arcane focus or a weapon from an enemy if they are not holding it.
The actual situation where this came up was prompted by an AT Rogue with the fey touched feat who used hex as a bonus action and hexed wisdom. I could not sneak attack because I won initiative and had to move. What I wanted to do was cast the hand and then take the enemies melee weapon, which I could have tried without the Hex (action cast - BA SOH), but with the hex I could give him disadvantage on his wisdom check making it more likely to be successful.