Honestly, the iron dagger grind is faster than you'd think if you do it right, but I get why it feels tedious. That said, there's no quest that dumps enough ore on you early to skip it entirely.
Your best bet is to mix it. Grab whatever ore you find naturally - there's iron veins scattered around (Halted Stream Camp is literally next to Whiterun if you haven't looted it), and loot weapons off bandits and draugr. Smelt those down and craft something useful instead of daggers. Steel plate armor, shields, whatever your build needs. It levels smithing the same way, just feels less pointless since you're actually gearing up.
One thing that helps: get the perk that lets you craft multiple items at once (the one in the smithing tree that speeds up crafting). Knocks a lot of the tedium out. And if you're playing with mods on PC, there's stuff that increases ore yields or makes smithing a bit less grindy, but sounds like you're going vanilla this time.
By level 30 you should have decent armor if you're actively crafting stuff you use. Just don't expect to hit Daedric or anything fancy - that takes a while. Steel and Elven will get you through most of the early-mid game fine.