It may depend on your garden (soil, moisture, amount of sun, etc) some, but a lot of it will depend on how long it was at Costco and how well or poorly it was cared for and whether it is bareroot or in soil. You will probably get a few flowers next summer but you probably won't get a larger vine with many flowers until two summers out.

I have seen them grow flowers even in the first year, but it is usually recommended not to let them do that. Just let it focus on giving energy to the roots. However, if you're not so tuned in to the daily efforts of the plant, it's not absolutely necessary to snip off any flowers that form in the first year.

But not every clematis root or plug will do that. I planted one at my mom's house 3 years ago. This is the first year it has put out blooms. The first year, I thought it was dead since we really didn't see any sign of it at all, and the second year, I saw a vine that maybe grew about 36", but no flowers.