You don't have a marketing idea you have a joint venture proposition.
If you have an advertising infrastructure (your product), then you would approach them through through their marketing agency, because that is a logistics issue not big picture thinking/strategy.
If you have a complimentary product you are selling and thought of a clever way to leverage other company's budget and brand to sell more you have a joint venture, you would go through the executive leadership in that company most likely.
If you are a single person with only an idea and no tangible measurable data to back your theories, you would be better off pitching the agency and hope they implement it. Typically an agency who has a contract for a campaign can deliver ads in any way as long as it remains true to the original intent and does not affect budget. At least that how our team did it in the past.

Also, you don't have a strategy, what you have are ideas or goals. Strategy gets thrown around so easily it has almost lost its meaning.