Do you have access to the Customizer? Or can you install a plugin? The inability to add even CSS code would be problematic. You could add style blocks within post and page content in text/code view, but then you cannot ever use the visual view because the CSS code will become corrupted.
Anyway, use your browser developer tool’s element inspector to identify the CSS that hides the menu and display’s the button. Override these rules so the menu always is displayed and the button never is. For example, in twentytwelve, the rule to show the button that you need to override is
.main-navigation ul.nav-menu.toggled-on, .menu-toggle {
display: inline-block;
}
Add the same overriding rule where ever you can, changing inline-block to none. If you can, the Additional CSS panel of the customizer is the best place for this. Do something similar for the code that hides the regular menu.