Description of the issue
We have often discussed in the past the need for a builder pattern for constructing circuits, for example see #3246 and #2775.

#6013 made a first attempt of abstracting out an important piece of circuit construction code into a free function - get_earliest_accommodating_moment_index.

This issue to discuss:

1. Where to best put the free function get_earliest_accommodating_moment_index.
2. Create a new circuit builder class that can generalize the utility provided by get_earliest_accommodating_moment_index and can be used in both Circut._load_contents_with_earliest_strategy and _stratify_circuit for efficiently constructing new circuits.

Cirq version

1.2.0.dev