[Written before I'd read your example; for advice relevant to that, see the PPS.]
The second, if you're referring to a definite period (definite article, see? )
You can refer to an indefinite time after 'the start', but then year would be plural: 'Years after the start, we noticed <thing>'.
PS It's anybody, though if you're surrounded by American English speakers this may be hard to remember! (The Br English /ɒ/ makes it easier to remember.)
PPS In this case you're referring to a particular period, but you need a preposition. So you would say something like 'During the years ...'. In a different context, you could use an indefinite expression: 'For years after the start ...<whatever-happened>, but later things started to go wrong'. (But be careful to say /fǝ jiǝz/; if you say /fɔ:/ it will sound as if you are starting to say something like 'Four years after the start, <something-happened>'!
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