The construction with "it will be better that" is a literal translation from the Spanish - the English we give is not at all literal.
Idiomatically in English when we use an impersonal expression like this one, it's always "it would be better" (which is neither the translation we give nor the translation that you propose). If you want to use the simple future in english then the grammatical and idiomatic construction would be "it will be better TO START xxx" so no use of "that" - to use "that" you need to use "it would be better".
There is no direct literal translation of this sentence possible because English tenses don't get used in the same constructions as the Spanish ones.
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