How to do outwards curves CSS?

Question

I am having trouble curving these corners. The grey area in the middle is going to be a video, and I need these edges to "curve outwards", so I can't use border-radius. Currently I am using border-radius on the top-right top-left and top-bottom-left elements to curve inwards, but I'm unable to curve outwards to make it seem as though it's all curving into each other.

This is what I have so far:

And this is what I need to recreate:

<section class="top-hero">
   <div class="top-hero__top-left">
      <a class="button" href="#">
         <span>View Site</span>
      </a>
    </div>
    <div class="top-hero__top-right">
       <a class="button" href="#">
         <span>View Site</span>
       </a>
    </div>
    <div class="top-hero__content"></div>
    <div class="top-hero__bottom-left"></div>
</section>

.top-hero {
  position: relative;
}

.top-hero__top-left {
  background: #fff;
  padding: 0 20px 20px 0;
  box-sizing: border-box;
  text-align: center;
  border-bottom-right-radius: 10px;
  position: absolute;
  top: 0;
  left: 0;
  z-index: 2;
}

.top-hero__top-right {
  background: #fff;
  padding: 0 0 20px 20px;
  box-sizing: border-box;
  text-align: center;
  border-bottom-left-radius: 10px;
  position: absolute;
  top: 0;
  right: 0;
  z-index: 2;
}
.top-hero__content {
  padding-top: 50%;
  background: lightgrey;
  position: relative;
  border-bottom-right-radius: 10px;
}

.top-hero__bottom-left {
  min-height: 100px;
  border-top-right-radius: 10px;
  background: #fff;
  position: absolute;
  width: 30%;
  z-index: 2;
  bottom: 0;
  left: 0;
}

.button {
  font-size: 14px;
  text-transform: uppercase;
  letter-spacing: 1px;
  font-weight: 600;
  text-decoration: none;
  background: lime;
  padding: 15px 35px;
  line-height: 1;
  display: inline-block;
}