Synthetic Stock Position

We say that being Long T-Bills + Equity Futures is the same as owning the underlying stock (I think?), but wouldn’t you need different initial cash outlays depending on whether you went down the synthetic route or the outright ownership route?

Example

Futures: The amount of cash I need to enter the forward contract is my desired investment amount * (1+RFR), e.g. 100mio. I will invest this today and grow it at the risk-free rate and will then have enough cash to pay for the stock at contract maturity.

Outright ownership: If I invested 100mio today in outright ownership, it would only grow at the div-yield + any price appreciation. I’d need to invest a slightly different amount (Future amount/(1+div_yield)) at the start of my time period.

So i see how it ends up with the same amount of contracts at future dates, but to do this would involve slightly different initial investments depending on the option you chose? Is that correct or am I missing something?

No they should be equivalent. The forward price includes all cash flows, including dividends. So the amount of cash required includes the dividend yield implicit in the forward price. Schweser has some theoretical examples showing how the math adds up.