There's no good way to do this. You'll have to iterate over all elements that might match what you want, then filter them out.
const starts = $('div').filter(function() {
return [...this.attributes].some(
attrib => attrib.name.startsWith('data-start')
);
});
console.log(starts.length);
console.log(starts[3]);
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div data-start-1="one"></div>
<div data-start-1="one"></div>
<div data-start-2="two"></div>
<div data-start-3="three"></div>
<div class="somethingElse"></div>
A much better approach would be to be able to select these elements using something else in common, like a class or another data attribute or a descendant of a container.
const starts = $('.container div');
console.log(starts.length);
console.log(starts[3]);
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div class="container">
<div data-start-1="one"></div>
<div data-start-1="one"></div>
<div data-start-2="two"></div>
<div data-start-3="three"></div>
</div>
<div class="somethingElse"></div>