Integrate the WordPress Media Uploader in Theme Options. Reference this function from your add_meta_box() callback

child-theme-settings.php

<?php

function upload_image_metabox() {
	
	echo '<p><strong>Upload image</strong></p>';
	echo '<input type="text" id="child_logo_url" name="' . $this->get_field_name( 'welcome-image' ) . '" value="' . esc_attr( $this->get_field_value( 'welcome-image' ) ) . '" size="50" />'; 
	echo '<input id="child_upload_logo_button" type="button" class="button" value="Upload Image" /> ';
	
	?>
	
	<script type="text/javascript">
	// JavaScript to launch media uploader, should be enqueued in a separate file
	jQuery(document).ready(function() {
		jQuery('#child_upload_logo_button').click(function() {
			wp.media.editor.send.attachment = function(props, attachment) {
				jQuery('#child_logo_url').val(attachment.url);
			}
		wp.media.editor.open(this);
		return false;
		});
	});
	</script>
	
	<?php
	
}

wp.media will only work if you add wp_enqueue_media();

https://codex.wordpress.org/Javascript_Reference/wp.media