Heroic strikes give you a chance of strike specific loot that drops at up to 335. 3 of Coins give you a chance of exotics up to 335. Challenge of elders gives you a chance of loot up to 335.
It'll take longer to reach max level than if you were to do the hard raid, but it's most certainly doable. That's how I managed to get 2 characters to 335 and one to 334 without a single hard raid.
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When I did this, I was primarily just grinding out engrams. Now, I understand these sytstems a little more. One thing I didn't know is how the dropping worked, but I already have a few 320 gear pieces.