Wait it out
As you propose, and Thomas Markov explains, wait the d4 hours for the NPC to regain consciousness.
Cleric in a bottle
The OP asks how, absent cleric spells, can the NPC be healed. One of the PCs might be carrying a potion of healing, either purchased or won as treasure. Whether they are willing to use it on an NPC is another question.
Cleric in a pouch
If one of the PC's has the Healer Feat (PHB 167 and possible if the PC is a variant human and started with it at first level) there are two different ways to restore the NPC to consciousness. If the Healer is the one to stabilize:
When you use a healer's kit to stabilize a dying creature, that creature also regains 1 hit point.
If another character has already stabilized the NPC, the Healer may also:
spend one use of a healer's kit to tend to a creature and restore 1d6 + 4 hit points
The party is far more likely to spend the 0.5gp for one use of a Healer's Kit than the 50gp for a potion of healing, in my experience.
Slap them awake
Possibly immersion-breaking, but if the party has a reliable way of stabilizing the NPC (eg., spare the dying cantrip) they can take the stabilized NPC, deliberately damage them to force them to start making death saving throws, and hope that they roll a 20 and naturally regain 1hp and consciousness. If not, stabilize them again and repeat until they do roll a 20 (or roll a 1 and immediately die).
Convince them to take a short rest
Rules-murky, but RAW say that you need to be at positive hp to take a long rest, while they put no such explicit condition on taking a short rest, and neither rest requires consciousness (in fact, a long rest requires that you spend most of it unconscious or semi-conscious). Whether or not you can spend HD while unconscious and heal yourself on a short rest turns on whether your DM considers such healing to be 'more strenuous' than 'eating, drinking, reading, and tending to wounds.' Both JC and Mearls have unofficially tweeted that spending HD to heal while unconscious is permitted (for the Mearls link, word-search on 'stabilized').
This method would require you to wait an hour, but one hour flat is better than d4 hours. As far as what your party can do to encourage the unconscious PC to spend its HD, well, roleplay. The out-of-spells cleric can pray, the barbarian can yell at the unconscious NPC, the fighter can dress their wounds, the bard can take their hand and with soothing words try to guide them back toward the light.