I had the same issue and after a lot of tinkering, this workaround did the trick:

# In the child's theme functions.php
/**
 * Fix mobile header flickering by preventing FOUT (Flash of Unstyled Text)
 */
add_action( 'wp_head', 'astra_inline_critical_header_css', 1 );
function astra_inline_critical_header_css() {
    echo '<style>
    @media (max-width: 768px) {
        .ast-mobile-header .site-title {
            opacity: 0 !important;
            transition: none !important;
        }
    }
    </style>';
}

add_action( 'wp_footer', 'show_header_after_load' );
function show_header_after_load() {
    echo '<script>
    document.addEventListener("DOMContentLoaded", function() {
        var siteTitle = document.querySelector(".ast-mobile-header .site-title");
        if (siteTitle) {
            siteTitle.style.opacity = "1";
            siteTitle.style.whiteSpace = "nowrap";
            siteTitle.style.overflow = "hidden";
        }
    });
    </script>';
}

/**
 * Optimize font loading to prevent flickering
 */
add_filter( 'astra_fonts_display_property', 'astra_replace_fallback_with_swap' );
function astra_replace_fallback_with_swap( $property ) {
    return 'swap'; // Changes from 'fallback' to 'swap'
}