How do I programmatically set contextual filters?

Contextual filters use query string params. You could hard code these into the URL. If using a Url object, you can pass a third argument ['query' => ['param1 => 'param1_value',...]]. Try setting a filter and seeing what the URL param name & value is after doing so.

In hook_views_pre_build(), you can also set the filter value directly:

$view->filter['filter_name']->value = 'filter_value';

It's helpful to have Xdebug so you can see the names of existing filters. If you don't have xdebug, try finding the correct filter name in the ->filter property, then find the desired filter value, and put 2 and 2 together.