About The Timeline and Backstory
First, the Westworld Park and the Hosts were not originally owned by Delos Corp. It was owned by Arnold Weber's and Robert Ford's company, Argos Initiative.
The season one backstory about Logan, a Delos EVP introducing William to park, where wealthy people like Logan can go to play, was not about a Delos investment at first, but rather William was was joining the Delos family by marrying Logan's sister, Juliet. Logan then saw Westworld as a rights of passage to William's manhood to prove he deserved to become apart of this elite family.
1.10 The Bicameral Man - Transcript:
LOGAN: I told you this place would show you who you really are. You
pretend to be this weak, moralizing little asshole, but, really,
you're a fucking piece of work.
WILLIAM: This place is remarkable. And I'm gonna make sure that our
company substantially increases our holdings on the park.'Cause this
place is the future.
LOGAN: Our our company, huh? Our company? My. Delos is my company, you
piece of shit!
WILLIAM: I think your father's gonna need someone a little more stable
to take over. You're reckless, Logan. Impetuous.
After having his heart broken in the park, William surpasses Logan's expectations to the point where William begins to see potential in what he believes (his beliefs are constantly contested) Westworld really is. In season two we learn how he was able to take over the family business and convince James Delos (Logan's and Juliet's father) to buy the park.
James Delos is first seen visiting Sweetwater early in the the park's
history. With the Hosts, including Dolores Abernathy and Teddy Flood
frozen around them, James and William have a conversation about the
potential of the park. William tells him that if James can't see the
potential for data-mining of the guests, then he is not as good a
businessman as he has heard. James likes William's courage at
challenging him, and invites him to tell him what kind of ideas he has
Later, James is at his retirement party, having seemingly passed over
Logan for control of the company in favor of William. James mentions
that he does not have much time left and coughs repeatedly, indicating
that he is ill.
Note: The highlight passage about "data-mining" the guests was also restated as the point of Westworld by another character in episode 2.07.