Write the specification first, then where facilities are, what to ask, and what to put on the agreement.
A co-packer makes or packs your product to your specification in their facility. Finding one is a specification problem before it is a search problem: a co-packer quotes against a written spec, and a brand that arrives with a sample and a feeling gets either no quote or the wrong one. This is how to get from the sample to the run.
The formula or bill of materials, the packaging and its dimensions, the unit and case sizes, the shelf life you need, the certifications the buyer requires, and the volume you can actually commit to. A co-packer decides in minutes whether a job fits their line. Without the spec they cannot decide, and they will quote the version of your product that fits their line rather than yours.
Industry directories by category, the trade show for your category (co-packers exhibit), your ingredient and packaging suppliers, who know which facilities run what, and the protocol's manufacturer role, where a facility lists its capabilities, minimums and lead times.
Minimum run, lead time, what certifications the facility holds, whether they run anything allergenic on the same line, who supplies ingredients, and what a trial run costs. Ask for two current clients and call them. A co-packer that will not name a client is telling you something.
Who owns the formula, what exclusivity was agreed, how quality is checked and by whom, what happens to your packaging and ingredients if you leave. Every dispute between a brand and a co-packer is one of those four, and each is cheap to write down before the first run and expensive after.