Use a priming tool to develop oil pressure without running the engine and turn the crankshaft over slowly by hand. It sounds like the lifters were installed without pre-oiling them, and it might take a long time for them to fill so they can be adjusted correctly. An empty lifter has trapped air in it, which is why at least some of them can be compressed by hand. Stovebolt hydraulic lifters, particularly the ones made recently in some third world country, are notorious for being defective. There are ways to work around those problems, but there's nothing easy or completely reliable about it.

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