No matter how liberal and broad-minded men claim to be, they will never appreciate women popping the question of going out on a date on the first meeting itself. Especially, in an arranged marriage scenario, you tend to judge the person based on their initial behaviour. So, there are good chances of him thinking of you as too 'fast'. Simply, stick to the conservative norms and let him take the lead (at least on this matter) and not vice versa.