Player investment and agreement
First off, you need to get the group agreeing that they want to play a game where characters matter and aren't just like videogame NPCs (people are just things to activate the next part of the adventure). For some players, this is the only way they know how to play, and you have to educate them to the variety of options out there.
This agreement is critical, because nothing else you can do will work without them actually being in on it. Since you are specifically asking for techniques that are not coded in hard mechanics, which are the most reliable method, you are effectively coasting 98% on player participation and 2% on your own actions.
NPCs are reasonable
The easiest way to get players to tie into NPCs is to give them likeable and unique NPCs. "Likeable" doesn't always mean nice, doesn't even mean they're on the same side as the players - they are simply characters who players can respect or enjoy their outlook on things - and part of that is these NPCs should be reasonable.
Reasonable means that friendly characters will try to help, to a limit, without even being asked, and unfriendly characters will oppose, but only up to a limit as well.
Most importantly, is that the players' reactions may cause these characters to shift - more or less friendly depending on the case. This makes NPCs feel more "real" and not like adventure markers in a videogame. Motivations are also particularly useful for interesting antagonists.
Now, one of the problems to this is that a lot of adventures are built on pre-set scenes or outcomes, which also means that the NPCs are highly limited in what they can do - if a character says too much, or changes sides, then the constructed adventure path falls apart, which then means a lot of NPCs end up being unreasonable. This becomes even more of a problem depending on the writing of the adventure as it is ("So wait, the Grand Priest wants us to stop the world from being destroyed, but won't give us a few Scrolls of Scrying? Why?")
When NPCs care, players care
Having NPCs actually care about the PCs and comment on it, is pretty much how this works.
A game I ran earlier this year had a girl who was orphaned who saw that one of the PCs did the same sword style as her dead older brother - she wanted him to teach her because it was her connection to her late brother. It was the combination of her personal motivation plus the admiration she had for the PC that the player really latched onto.
These characters also have problems of their own, some of which aren't directly tied to the PCs and after the players have gotten attached, they may begin taking their own steps to help the NPCs without questions asked.
Of course a key point to this is whether your overall game is about emotional ties or not in the first place. If not, you can expect these things to fall by the wayside rather than become a focus of play, and also, many players may have never encountered such play and therefore are totally unfamiliar with how to engage with it. This is pretty much the big reason why mechanics-based solutions tend to work more reliably because it often is hardcoded in a way players can't avoid or forget about it.