It´s possible create a full-width slider with CPT Bootstrap Carousel plugin?
Yes, but then you have to move it somewhere outside
.container because otherwise it will be limited to its size (1170px). So if you add slider shortcode using do_shorctode right after closing
</nav> and before opening content container it should cover the entire screen. Of course, some tweaks CSS tweaks might be required but it should work as long as image sizes are enough to cover the entire screen.
Default slider shortcode using do_shortcode inside php file would look like this:
<?php echo do_shortcode('[image-carousel twbs="3"]'); ?>