You can add a pseudo element in the <label> tag, and use some position and padding tricks for the visual. Using a svg for background is just the same as using an image.
label {
position: relative;
}
label:before {
content: "";
position: absolute;
left: 10px;
top: 0;
bottom: 0;
width: 20px;
background: url("data:image/svg+xml,%3Csvg xmlns="http://www.w3.org/2000/svg" width="25" height="25" viewBox='0 0 25 25' fill-rule="evenodd"%3E%3Cpath d='M16.036 18.455l2.404-2.405 5.586 5.587-2.404 2.404zM8.5 2C12.1 2 15 4.9 15 8.5S12.1 15 8.5 15 2 12.1 2 8.5 4.9 2 8.5 2zm0-2C3.8 0 0 3.8 0 8.5S3.8 17 8.5 17 17 13.2 17 8.5 13.2 0 8.5 0zM15 16a1 1 0 1 1 2 0 1 1 0 1 1-2 0'%3E%3C/path%3E%3C/svg%3E") center / contain no-repeat;
}
input {
padding: 10px 30px;
}<label>
<input type="text" placeholder="Search">
</label>