Does the core science req require 8 hours of consecutive science?

Or could I do like astronomy then geology and have it met?

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Eight semester hours in courses approved for the natural science (NS) designation, including two semester hours of laboratory experience. The NS designation indicates that the course applies quantitative or inductive reasoning to a subject within the natural sciences.
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It doesn’t say that they must be sequenced. So a student can take Bio and Chem or X and Y to satisfy.

Altho, could a sequence of science classes satisfy the ‘depth study’ requirement, and then you’re killing two birds with same stone?

You should look at CLEP testing. You might be able to CLEP out of Biology or Chemistry.

A sequence of science classes doesn’t satisfy the “depth study” requirement. I assume by the way you refer to it that you’re in the college of engineering. From the catalog, this is the engineering requirement: “A six-hour discipline depth study is required and may be taken in either HU, L, and FA or HI and SB.” If you’re in one of the other colleges, the sequence needs to be in either Literature or History.