Manufacturing experience can translate very well if you frame it around the problems you solved rather than the factory setting itself. Cost reduction, capacity planning, quality improvement, supply chain decisions, capital allocation, and operational transformation are all highly relevant consulting problems.
The risk is presenting your background as purely technical. Your resume and interview stories should show the business consequence of your work: revenue protected, cost removed, throughput increased, teams led, or decisions influenced.
For a generalist role, make it clear that your skills travel beyond manufacturing. Structured problem solving, stakeholder management, analytics, and implementation are portable. Your industry knowledge can be an advantage, but it should not be the only reason the firm can imagine using you.