margin-top only when the flex item is wrapped

You can add some margin-top to both flex items, and a negative margin-top of the same amount to the flex container.

This way, the negative margin of the flex container will neutralize the margin of the flex items at the first line, but not the margin of the items that wrapped to other lines.

.container {
  margin-top: -30px;
}
.item-big, .item-small {
  margin-top: 30px;
}

.container {
  display: flex;
  flex-wrap: wrap;
  justify-content: space-around;
  margin-top: -30px;
}
.item-big, .item-small {
  margin-top: 30px;
  background: red;
}
.item-big {
  background: blue;
  width: 300px;
}

<div class="container">
   <div class="item-big">
      FIRST BIG ELEM
   </div>
   <div class="item-small">
      SECOND SMALL ELEM
   </div>
</div>

Nowadays there is overall support (MDN) for the css (row-)gap property in flex layout containers which this answer proposes. The way to go 🙌🏼.