No, the weapon would not disappear (but does lose its magic)
Not all "supernatural" effects are magical
So you might look at an ability that summons a weapon from nowhere and think that that is definitely a magical ability (I thought the same thing), but that is not actually a safe assumption.
In fact, not everything that seems magical is actually considered as such by the rules. There are many abilities and effects in the game that are very supernatural, but not a result of magic. For example, a paladin's aura and lay on hands ability are not magical despite being clearly supernatural (see Are a Paladin's auras considered magical for the purpose of Anti-Magic Field?). And neither are many monk ki abilities, dragon breath attacks, and many more features and abilities. All these abilities work flawlessly inside an antimagic field.
So how do you determine what is magical and what is not?
Fortunately, the Sage Advice Compendium outlines the exact way to determine if something is magical or not specifically for the purpose of antimagic field and related effects:
Determining whether a game feature is magical is straightforward. Ask
yourself these questions about the feature:
Is it a magic item?
Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
Is it a spell attack?
Is it fueled by the use of spell slots?
Does its description say it’s magical?
If your answer to any of those questions is yes, the feature is
If the answers to all the above questions are "no" then that ability is not magical.1
Pact Boons and Pact of the Blade are not magical abilities
Pact Boons are described as:
At 3rd level, your otherworldly patron bestows a gift upon you for your loyal service. You gain one of the following features of your choice.
Nowhere in this description or in the specific description of pact of the blade does it specifically call out that the ability granted by the patrons is in any way magical.
Neither Pact Boons in general nor the pact of the blade boon have a "yes" for any of the Sage Advice questions listed above. The only one that is even a little bit unclear is the question on if it is a magical item. The reason this is "no" is that we are trying to ascertain whether the ability that creates the weapon is magical and it doesn't matter for that purpose if the weapon created in the end happens to be magical. Though that will come into play in the next section.
All this means is that these abilities that are creating the pact weapon are not magical effects.2 And because the pact weapon was not created using magical effects, it is not subject to any effects that would cause them to vanish.
Since the pact weapon is created by a nonmagical ability, it does not disappear in an antimagic field
There are two ways to create pact weapons as granted by the Pact of the Blade feature:
Create one from nothing (which is the one that is focused on in the question)
Use a ritual to make an existing weapon into a pact weapon
However, since they are both created by the same nonmagical ability, neither method of weapon creation would leave the weapon vulnerable to disappearing in an antimagic field.
Addendum 1: Any magical properties of the pact weapon will be suppressed in the antimagic field
Even though pact of the blade is not a magical ability, the weapon it creates is magical:
[The pact weapon] counts as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.
Thus, the weapon will have an interaction with antimagic field as is described in the spell effect:
The properties and powers of magic items are suppressed in the sphere. For example, a longsword, +1 in the sphere functions as a nonmagical longsword.
Being a magic item, the pact weapon will thus have its ability to overcome nonmagical damage resistance be suppressed (along with any other explicitly magical abilities the weapon might have). Still, it will not vanish.
Addendum 2: There appears to be an edge case with Improved Pact Weapon3
Improved Pact Weapon is an invocation that, among other things, allows the warlock to create bows as their pact weapon (which is not allowed by default). The tricky part comes from the fact that the book explicitly says that invocations are all magical abilities so it puts this as a difficult edge case.
It is not super clear what would happen if one were to walk into an antimagic field with a bow pact weapon that you created from nothing (not an from a real weapon). However, a reasonable outcome would be that the bow disappears in the field, but the warlock retains the ability to summon it back, just not in any of the forms granted by Improved Pact Weapon. And the forms will remain restricted until the warlock is out of the field.
1 - This might seem like a logical fallacy, but it follows the intent of WotC's own logic. For proof of this, see how the Sage Advice Compendium uses the rule above to analyze a dragon's cold breath attack to see if it is a magical ability:
Let’s look at a white dragon’s Cold Breath and ask ourselves
those questions. First, Cold Breath isn’t a magic
item. Second, its description mentions no spell. Third, it’s
not a spell attack. Fourth, the word “magical” appears nowhere
in its description. Our conclusion: Cold Breath is not
considered a magical game effect, even though we know
that dragons are amazing, supernatural beings.
2 - The Pact Magic and Eldritch Invocation features, on the other hand are both explicitly called out as being magical abilities and thus are suppressed in the antimagic field.
3 - Found, very cleverly by @Gandalfmeansme