My theory is that good engineers want to work with people they can learn from, work on interesting problems and see the fruits of their labor appreciated and used. Startups have a huge advantage here over large established companies. Hopefully during the interview process you showed off all the great people in your company, the involvement in product design your engineers have, and the high level of responsibility each engineer has.
At Gigantic Co the average quality of the engineers is not going to be as high (it can't be with 1,000 engineers), the size of the problem each individual engineer gets to work on is smaller (bureaucracy loves slicing problems into ever thinner pieces and distributing them around to too many people), some product manager is telling them exactly what to build, and the chance for personal fame is low.
What Gigantic Co can offer is more cash and the perception of stability. If a candidate just wants cash, you're going to lose them to the big companies and so be it. You didn't want them anyway. You're building equity value for the future and you want engineers who think the same way.
The risk perception argument is a tougher one to win, though it really is a bogus argument. There is effectively 0% unemployment for good engineers. So the only real career risk for an engineer is opportunity cost of not working on something interesting. There's effectively no risk that the engineer would be unemployed for long if your startup blows up.
Assuming you code tested the candidate, you know they are great and so you can invest a lot of effort into personally recruiting them. You can have your CEO or VCs call the candidate -- many candidates will be flattered by the attention. Candidates may also appreciate hearing more about the business strategy for the company, hearing why the VCs invested etc.