Having somebody else make it
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Contract filling is a well-established route in this category and the cheapest way past the hand filling ceiling.
What a co-packer is doing for you
Buying materials, making to your formula, filling, labeling and often packing to a case.
What they are not doing is developing your product. A co-packer will make what you specify; they will not tell you your formula grains, and they will not own the consequence if it does.
What they need from you
A formula in percentages with the grade and supplier of every material.
A process with real numbers, not "melt and pour".
A specification: what a good unit is, so there is something to accept or reject against.
Approved packaging components, and label artwork that is already compliant.
Which is why the recipe-to-product work pays twice. A maker with a real formula document can be quoted in a week; a maker with a recipe cannot be quoted at all.
Minimums are the constraint
Co-packer minimums are usually thousands of units per run, per SKU. Three flavors at minimum is a lot of finished stock and a lot of cash.
And a run is a run: you cannot reorder two hundred in a hurry. Plan inventory against their lead time rather than against your sales rate.
The regime follows the product
If the product is an OTC monograph drug, the filler has to be operating under cGMP and registered as a drug establishment. Not every cosmetic filler is, and it is the first question to ask rather than an assumption to make.
Their registration does not remove your obligations as the firm named on the label. You are responsible for what is made on your behalf, which is why the specification and the acceptance criteria matter more in this arrangement, not less.