The phrase "acknowledge that without" is correct and usable in written English.
It can be used when you want to emphasize the importance of a particular element or condition that is necessary for something else to occur or be true.
Example: "We must acknowledge that without proper funding, the project cannot succeed."
Alternatives: "recognize that without" or "admit that without".
But you can't acknowledge that without also acknowledging the time-tested rigor of modern science and all that it has accomplished -- and that it is far more likely that science is right here.
Its commanders acknowledge that without this support, it could not function.
Yet they acknowledge that without pressure from Kabul, little will move forward.
It's at this point that we should acknowledge that without Fox Sports, the Big Bash would not have reached this point.
They acknowledge that without £13.9m profit made selling players, principally Wilfried Zaha to Manchester United in January 2013, the club would have made a £7.7m loss.
Some veterinarians who administer the drugs acknowledge that without steroids some horses wouldn't be able to stand the wear and tear of the racing circuit.
Yet it's possible to be dissatisfied, even angry, about the way the financial bailouts have worked, while acknowledging that without these bailouts things would have been much worse.
In November 2007, the Commission officially decided to suspend the infringement case against Belgium [ 15], acknowledging that without this restrictive measure, a problem could arise in the future for the quality and the sustainability of the Belgian health system.
Education in global health thus becomes a means to 'mobilise the commitment of the workforce' [ 5] rather than an end in itself, acknowledging that without this mobilisation the health workforce can be 'an enormous source of resistance to change, anchored to past models that are convenient, reassuring, profitable and intellectually comfortable' [ 5].
The Fifth Circuit judges acknowledged that women without much money would be more affected by the law than others: they might not have a car, or a way to take a day off from work to drive six hours.
