Construction giant John Holland identified in internal documents that the union's influence had helped get Mr Andrews elected.
Mr Andrews served as premier from 2014 through to his resignation in 2023.
An August 2021 John Holland memorandum was described on Monday to a royal commission into alleged corruption on taxpayer-funded construction sites in Victoria.
The document laid out the company's international relations strategy in Victoria and identified the CFMEU and government's relationship as critical to better positioning the company.
"The CFMEU enjoys a significant level of influence within the state government," the memorandum stated.
"It's a level of influence not seen in previous years, and is unlikely to diminish in the next and subsequent elections.
"This means our engagement with the CFMEU should be seen as part of a broader strategy to better position our business with the state government."
An earlier, 2017 memorandum identified "the union movement played a critical role in the election of the government, both organisationally and financially".
The royal commission is probing whether on-site safety and entry powers were used as industrial leverage.
Weeks of expected hearings ahead of the November 28 state election will investigate the involvement of organised crime and the construction union's alleged grip on worksites.
In opening Monday's hearing, counsel assisting Chris Young KC said several submissions received by the commission appeared "on their face" to be untrue and some disclosed conduct that appeared to be misconduct, corruption or crime.
November's sessions will examine events at Sunbury's Gap Road project, which involved the removal of a level crossing and the construction of a new rail bridge and underpass.
The Sunbury project was delivered by the Rail Infrastructure Alliance, with the commission to focus on the rail occupation in June 2022.
Under the alliance, industrial relations responsibilities were shared between participants which included the state government, as the project's owner.
In particular, the inquiry will examine events during that month, including a meeting at the CFMEU's offices after a two-day stoppage.
Commissioner Chris Kourakis KC said the arrangements made at that meeting, what they cost and who paid for them would be the subject of inquiry.
"We will examine how much the state knew and what it didn't, and what it did and didn't do about circumstances unfolding there," he said.
Mr Young outlined seven themes which would be the focus of the commission.
They include what the state did in response to reports of alleged unlawful or corrupt conduct by contractors, with some saying they received no response to years of formal notices.
It will also examine how contractors managed industrial relations disputes.
As of Friday the commission has issued more than 200 notices, resulting in the production of more than 110,000 documents.
Evidence received by the commission so far suggested apparently legitimate businesses paid large amounts to people associated with organised crime, Mr Young said.
"The services they paid for appear to involve little more than intimidation and menace," Mr Young said.
He described it as "no small task" to rid the construction industry of its alleged links to organised crime.
Premier Ben Carroll vowed to set up the $50 million royal commission as his first act in government after he toppled predecessor Jacinta Allan, who had rejected widespread calls to launch a probe.
Ms Allan and her predecessor Daniel Andrews had legal counsel representing them at the commission on Monday, with both open to being called to give evidence.
The commission's final report is due in August 2027.
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