Well, with certain words it's simply impossible to start a grammatical sentence: one such word that comes to mind is "ago".
It always comes after other words (e.g. "one hour ago"), never at the beginning of a sentence or clause.
[Before someone points it out: note the use-mention distinction .
A sentence like
'Ago' is a word you cannot start a sentence with.
starts with the word "'ago'" and not with the word "ago".]
But if your question "Is there any valid rule discouraging the use of a certain word to start a sentence?"
(emphasis mine) implicitly restricts attention to words that can grammatically start sentences, then it's not clear what it would take for a rule that discourages something grammatical to be "valid".
Certainly there exist people who disapprove of certain words starting sentences for their own idiosyncratic reasons, such as the "but" I started the previous sentence with.
Are these "rules" valid?
I wouldn't consider them valid, but I don't know what valid means to you. :-)
english.stackexchange.com/users/77/ShreevatsaR
In school we were taught to "never begin a sentence with 'and', 'but', or 'so'".
But I do anyway.
And so do a lot of other people.
english.stackexchange.com/users/1102/Graeme Perrow
The past tense of many verbs make no sense as the first word in a sentence: 'went', 'tried', etc., unless it's in a context where sentence fragments are OK: 'Where you been?', 'Went to the shops'. '
Ago' is a particularly nice example because it wouldn't even work in an informal sentence fragment.
english.stackexchange.com/users/8101/jaybee
Is there any valid rule discouraging the use of a certain word to start a sentence?
There's a rule (can't say if it is valid or not)
that numbers, no matter how long, at the start of a sentence should be written out in words, Seven thousand,
four hundred and seventy-six trombones led the big parade so some people avoid putting numbers there.
Also, it's a bit odd to capitalize terms which are computer commands which won't work if they are capitalized:
Ls is how you get a listing of your files
so some people might avoid putting those terms at the start of sentences.
english.stackexchange.com/users/None/
Use of greek letters or numerals is discouraged.
See also Is it okay to start a sentence with a Greek letter (variable)?
english.stackexchange.com/users/2559/David LeBauer
Is there any rule you think is valid that discourages the use of a certain word to start a sentence? Because I suspect the answer is no. But it would be good to have a blanket answer to this kind of question.
Is there any valid rule discouraging the use of a certain word to start a sentence?
english.stackexchange.com
<grammaticality><sentence><conjunctions><sentence-starts>
english.stackexchange.com/questions/2765
english.stackexchange.com/users/122/cindi
Whilst there may not be a valid rule discouraging the use of a certain word to start a sentence, there are certain words with which it is impossible to start a sentence, such as "ago". Certain words have been discouraged in this sense in school, such as "and" or "but", but many people do not follow this rule. The use of Greek letters or numerals is also discouraged. There are no rules but it is impossible to start a grammatical sentence with certain words, such as "ago", which can only come after other words.
Whilst there may not be a valid rule discouraging the use of a certain word to start a sentence, there are certain words with which it is impossible to start a sentence, such as "ago". Certain words have been discouraged in this sense in school, such as "and" or "but", but many people do not follow this rule. The use of Greek letters or numerals is also discouraged. he past tense of many verbs make no sense as the first word in a sentence: 'went', 'tried', etc., unless it's in a context where sentence fragments are OK: 'Where you been?', 'Went to the shops'. 'Ago' is anothere example. Schools used to teach "never begin a sentence with 'and', 'but', or 'so'". Use of  greek letters  or  numerals  is discouraged.
With certain words it's simply impossible to start a grammatical sentence: one such word 'ago'. However, it is also frowned upon by some to start a sentence with 'and', 'but', or 'so'. There are certain words with which it is impossible to start a grammatically correct sentence. Also, traditionally, people have been discouraged from using words like "and", "but", "so", greek letters or numerals to start sentences.
It's impossible to start a grammatical sentence with certain words, such as "ago", which can only come after other words. We are often taught to "never begin a sentence with 'and', 'but', or 'so'" but in reality many people ignore this. It is impossible to start a sentence with the past tense of many verbs e.g. "went" except in sentence fragments. Use of greek letters or numerals at the start of a sentence is discouraged.
he past tense of many verbs make no sense as the first word in a sentence: 'went', 'tried', etc., unless it's in a context where sentence fragments are OK: 'Where you been?', 'Went to the shops'. 'Ago' is anothere example. Schools used to teach "never begin a sentence with 'and', 'but', or 'so'". Use of  greek letters  or  numerals  is discouraged.
With certain words, it is impossible to start a grammatically correct sentence. At school, some students were taught never to begin a sentence with words like "and", "but", or "so". The use of greek letters or numerals at the beginning of sentences is discouraged.