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The phrase "access to the first" is grammatically correct and can be used in written English.
It can be used when referring to the ability to reach or obtain something that is the first in a series or category.
Example: "To proceed with the project, we need to ensure access to the first set of data collected during the research."
Alternatives: "entry to the first" or "availability of the first".
Exact(56)
Wheelchair access to the first floor.
There is also no lift access to the first floor.
WHEELCHAIR ACCESS Complete access to the first floor, with an elevator to the second, though one of the dining rooms upstairs has two stairs.
Her exchange with al Masri is still developing, and we non-Arabic readers only have access to the first of the Taliban writer's letters.
Back in Washington DC, we immediately began sending requests to the White House press office for access to the first meeting between Barack Obama and Donald Trump.
Under the new rules, retirees will not be able to roam everywhere freely but will be allowed unescorted access to the first two floors.
A major Japanese bookshop chain is taking a stand against the increasing dominance of online retailers such as Amazon by restricting their access to the first print run of a new essay collection by Haruki Murakami.
Similar(4)
An elevator permits wheelchair access to the first-floor dining room and restroom.
We have no access to the first-hand stories of its citizens, so we rely on western writers, whether of novels, such as Adam Johnson's Pulitzer prizewinning The Orphan Master's Son, or of journalism.
Baker gives far more emphasis than Cameron to the plight of the lower-class passengers in steerage, trapped below by iron gates preventing their access to the first-class decks and potential rescue.
There are plenty of other options—every legacy airline offers some kind of credit card that comes with priority boarding and sometimes even access to the first-class check-in lane.
More suggestions(22)
access to the sixth
access to the third
availability to the first
enrolment to the first
connection to the first
consultation to the first
access to the prior
accessibility to the first
access to the initial
admission to the first
exposure to the first
access to the strongest
access to the smartest
access to the largest
access to the biggest
access to the first ever
access to the earliest
access to the highest
access to the nearest
access to the worst
blinded to the first
access to the right
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com