Yes, I did it. To do this, I created the necessary dialogs programmatically with the support of a bean. I know that this is not the best practice, but at this moment I think this is only a possible solution. First of all, I added one panel, which is a container for dialogs on my JSF page. Then, with bean support, I have a code like this:
UIComponent panelGroup = facesContext.getViewRoot().findComponent("panel_id");
Dialog dialog = new Dialog();
dialog.setHeader("Sample");
dialog.setVisible(true);
dialog.setMinimizable(true);
...
panelGroup.getChildren().add(dialog);
...
RequestContext requestContext = RequestContext.getCurrentInstance();
requestContext.update("panel_id");
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