As we saw with the BasemapGallery widget example, in this example a BasemapGallery component is embedded within an Expand component. Note the setting of three attributes on the Expand component. The position attribute is self-explanatory. The mode can be either "floating", as shown here, or "drawer", which causes the basemaps to appear in a box filling much of the bottom of the window. The close-on-esc attribute controls whether the user can close the gallery by pressing the Esc key on the keyboard. As a Boolean attribute, you should simply refer to it by name (i.e., don't say close-on-esc="true") to set the attribute to true or omit it to set it to false.
You can have the gallery displayed when the map loads by setting the Boolean expanded attribute to true.
See the Pen BasemapGallery_component by Jim Detwiler (@jimdetwiler) on CodePen.