Learn English – Proper use of “Because of” followed by a “verb + ing”

The verb start takes complement clauses with either the marked infinitive or -ing forms, and there is no consistent difference in meaning between the two.

Consequently, both of your examples are grammatical. However, the version with the infinitive will usually be better, as it avoids using two -ing forms close to each other. This preference is generally acknowledged in contemporary linguistics and goes by the name horror aequi principle, a Latin phrase meaning, literally “aversion to the same thing”:

The horror aequi principle involves the widespread (and presumably universal) tendency to avoid the repetition of identical and adjacent grammatical elements and structures. —Gunter Rohdenburg, “Cognitive complexity and horror aequi as factors determining the use of interrogative clause linkers in English”, in Rohdenburg and B. Mondorf, Determinants of Grammatical Variation in English, 2003.

Another article in the same volume, U.Vosberg, “The Role of extractions and horror aequi in the evolution of -ing complements in Modern English”, states that

In many languages, we observe a strong aversion to the (immediate) co-occurrence of identical or similar grammatical structures. Thus, the establishment of -ing complements has been significantly delayed after matrix verbs appearing in the shape of -ing forms themselves. Such contexts tend to favour either the to-infinitive as verb complement or other alternatives (like nominal objects or finite clauses).

I assume your confusion comes from failing to distinguish two different words spelled to.

The examples in your question aren't exceptions. They contain the preposition to:

The key [ to being more productive ] is ...
I look forward [ to seeing you ].
He admitted [ to taking the money ].
Scientists are closer [ to being able to ... ].
seven steps [ to reaching your goals ]

In each case, the -ing form of the verb is what is traditionally called a gerund. When the verb is in its gerund form, the clause as a whole functions very much like a noun phrase.

Each of the bracketed phrases is a preposition phrase.

This should be distinguished from the infinitive marker to:

I want [ to eat as many sandwiches as possible ].
I'd like [ to visit New York ].

In each of these examples, the bracketed portion is a to-infinitival clause.

The word to in these examples marks the clause as infinitive; the -ing form is not possible here.