Some of us have faith that we shall solve our food problems with genetically modified crops newly or soon to be developed.
The 'newly or soon' modifies '(to)be developed' in front of 'to'. Can adverbs modify infinitive verbs in front of the 'to'?
Some of us have faith that we shall solve our food problems with genetically modified crops newly or soon to be developed.
The 'newly or soon' modifies '(to)be developed' in front of 'to'. Can adverbs modify infinitive verbs in front of the 'to'?
"Some of us have faith that we shall solve our food problems with genetically modified crops newly or soon to be developed."
There is nothing wrong with the sentence. "Newly" modifies "developed". The sentence could also be written more explicitly like this:
"Some of us have faith that we shall solve our food problems with genetically modified crops newly developed or soon to be developed."
You questioned whether adverbs can "modify infinitive verbs in front of the 'to'". That question doesn't arise in respect of "newly", because "newly" doesn't modify "to be". It may arise in respect of "soon", although "soon-to-be" (hyphenated by Oxford) is better regarded as a set phrase and treated as an adjective: Oxford Dictionaries ( https://www.lexico.com/definition/soon-to-be ) says, "soon-to-be adjective, attributive Planned or destined to have a specified position or quality in the near future."
If the sentence were "They are soon to be developed", on the other hand, it would be unhyphenated and "soon" would be more clearly an adverb. ("Newly to be developed" would sound rather awkward.)
In general, adverbs certainly can modify infinitives: "It was important seriously to consider the proposal" is correct (albeit stilted) English. (We would, however, prefer to say "It is important to consider the proposal seriously" or "It is important to seriously consider the proposal". The latter pattern was once scorned as a "split infinitive", but is now generally considered acceptable except perhaps in the most formal contexts.)
This sentence is grammatical. There is nothing wrong with putting an adverb before the infinitive to. It was more common in the 19th century, but it is still used and still considered grammatical.
It is, however, an awkward sentence because it needs to be parsed
crops newly (or soon to be) developed,
while the first parsing you try when you read it is likely to be
crops newly (or soon) to be developed,
and that gives you the construction newly to be developed which is wrong, because newly means that the crops have already been developed, while to be means that the crops have not yet been developed, so this is contradictory.
So it's a sentence that you should probably rewrite if you notice this problem (you could easily solve the problem by putting commas on either side of "or soon to be"). However, Google can find a number of times when native English speakers have written "newly or soon to be", and readers should generally be able to understand this construction.
Some of us have faith that we shall solve our food problems with genetically modified crops newly or soon to be developed. [BUZZER]
Some of us have faith that we shall solve our food problems with newly developed or soon-to-be developed genetically modified crops. [Correct]
OR
Some of us have faith that we shall solve our food problems with genetically modified crops that have been newly developed or are soon to be developed. [Correct but heavier]
Another example from the Internet:
Edap2007 is a company whose main purpose is to invest in unlisted companies featuring a large component of innovation and high growth potential, whether they are well-established companies, up-and-coming companies, or newly formed or soon-to-be-formed companies. Edap2007 works with the teams running the companies in creating value and in providing...[bolding mine]
Another example (mine)
freshly painted or soon-to-be painted rooms
When one wishes to pre-position a phrase like: that was soon to be painted, it must have dashes:
That is: canvases that are soon to be painted.
That is: films that will soon be released.
newly or soon to be developed GMO crops does not work.
The verb has to be repeated because otherwise you are saying: newly crops and soon-to-be-developed crops. And you are not thus saying: newly developed crops or soon-to-be-developed crops**.
Note: The reason the sentence is wrong has zero to do with an adverb in front of to. "soon to be developed" or soon to be [verb]" is a set phrase in English. It's FINE.
What isn't fine is: [...]crops newly or soon to be developed. [BUZZER!!]