Let me restate your question for clarity from a grammatical perspective: Isn’t there a right time when the article “the” can be omitted as modifier of the subject noun in a sentence like “The United States has gone one step further to make April National Autism Awareness Month”? In short, can we construct it this way: “United States has gone one step further to make April National Autism Awareness Month”?
My answer to that question is a categorical “no.” Stylistically, with writing newspaper headlines as a notable exception, there isn’t a right time to do that. We can’t write or say “Philippines is an archipelago of 7,100 islands” either. We need the article “the” before the geographical noun to make that sentence look and sound right: “The Philippines is an archipelago of 7,100 islands.”
Indeed, the United States and the Philippines—along with the United Arab Emirates, the Netherlands, the West Indies, and the Dominican Republic—are among the very few exceptions to the general usage rule that the article ‘the” shouldn’t be used before the names of countries and geographical territories. This is why we don’t read or hear people saying “the China,” “the Japan,” “the France,” and “the Germany” when using these names; the norm is to simply say “China,” “Japan,” “France,” or “Germany.”
Are there hard-and-fast rules then for when or when not to precede a geographical or territorial name with the article “the”?
There are three well-accepted stylistic conventions for this: (1) When the name of the country is in plural form—meaning that it ends in “s”—it is normally preceded in both written and spoken form by “the,” as in “the Philippines” and “the Netherlands”; (2) When the name of the country denotes a political entity, it should be preceded by “the,” as in “the Czech Republic” and “the Dominican Republic”; and (3) When the country is named after the fatherland or motherland—the so-called “patria”—the name doesn’t need the article “the,” as in “Britain,” “France,” “Russia,” and “New Zealand.”
An exception to Rule 1 is the seemingly plural-sounding Barbados, the name of that sovereign island-country in the Lesser Antilles; the accepted usage is not to precede that name with a “the.” We should also take note that contrary to popular usage, the country name Ukraine shouldn’t be preceded by “the.” Once commonly used in English, “the Ukraine” is now considered inappropriate, so just say or write “Ukraine” when using that country’s name in a sentence.