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The decision to till before winter or after depends on factors like weed control and soil aeration. Tilling before winter exposes weed roots and enhances soil aeration, while tilling in spring preserves soil structure and avoids disturbing beneficial organisms. When incorporating manure, it's generally beneficial to do so in the fall before winter, allowing it to break down and enrich the soil over the dormant season.

This collection of articles will offer more information on preserving your soil health:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers

If the manure was not composted, you should avoid harvesting vegetables for at least four months. A better scenario would be to put it down in the fall or winter for a spring garden. But composted manure is best because it eliminates weed seeds and disease pathogens if it is heated to 140 degrees F for a sustained time. Here is more:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/using-fresh-manure-in-gardens.htm

https://www.gardeningknowhow.com/composting/manures/manure-pros-cons.htm

https://www.gardeningknowhow.com/composting/manures/the-benefits-of-manure-in-your-garden.htm

Even using that much manure, if it was composted, could make the garden too rich and not appropriate for the flowers or vegetables you intend to grow. If you now have access to soil, you could add some garden soil to the mix.