The question linked in the comments answers the question if you can, and that is you can omit in the opening <html>
tag. However...
You shouldn't.
As the answers in this question and the question linked above show, the rules around when you can or cannot omit certain tags are long and lawyer-esque.
Written code isn't just for machines its for people too. This isn't to suggest that HTML should be human-readable without a browser, that's farcical, but it should be programmer-readable and there is a difference.
This is perfectly valid HTML:
<!DOCTYPE HTML>
<title>Hello</title>
<p>Welcome to this example.</p>
However, without consulting the spec I am not immediately sure where each element will be in the computed DOM, for the curious its equivalent to:
<!DOCTYPE HTML>
<html><head><title>Hello</title>
</head><body><p>Welcome to this example.</p></body></html>
However, if time is at a premium (and programmer time is almost always more expensive than computing time nowadays) then knowing quite clearly what a document is doing is vital.
No doubt someone will ask, what about when space or transmission speed is at a premium. In those cases thorough profiling to determine the exact bottleneck is important, and on the fly compression, good caching of HTML, or even automated removal of elements using a library will all be vastly superior options to removing tags in source code that is to be written and interpreted by people.