Hmmm... I see some implication here.
So, the "most possible" event trigger is the Gulf of Tokin Incident. OTL, there wre "two attacks" against the USS Maddox by Vietnamese People Navy. The first one was on 2 August 1964, "the second" is on 4 August. Of course, USA being USA, made up the second date, but with a bit more "colors" this time.
*Note: OTL - the USS Maddox was just 6 nautical miles from the shore, basically invading the sovereign of DRVN then. How serious was that? American, please imagine a Soviet warship appearing 6 nautical miles from the California or New York shore. Her mission? Unknown, but common sense dictates that she was carrying out intelligence operation against DRVN
So, in this ATL, the second (the "trigger") is still unlikely to happen, but the USS Maddox is "said" to sustain heavy damage. The US Congress pass the Resolution, allowing a full invasion (it was just a "blank check" in the OTL)
I'd say the US would send in 1 Marine Division, support by a lot of Air force and Navy. Taking control of the shore is easy (especially in the "bottleneck" region in the southern of Northern region). However, moving in-land would be a challenge.
Guerrilla tactics and the destroying of any critical roads can hamper the advance of the US greatly. At that time, the infrastructure of Vietnam was not very develop, decreasing the mobility of any armoured forces.
The paratroopers can be deployed to seize Hanoi (DRVN capital), but the appearance of the population (very anti-invaders) would put them in a hard pinch.
The Air force and Air wing of the Navy will be the "luckiest" because the anti-air units of PAVN were still in their infant stages (OTL, it was roughly 4 years later that they could stand and fight on their own effectively)
The NLF/VC in the South would use this chance to strike at the support bases, diverting US resources on different locations.
The regular forces of PAVN will stage in the west-northern region of Vietnam, with the advantage of terrain, they could hold out and preserve their strength, but lack the main drive to effectively push the American out.
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All in all, I'd say that USA had a fair chance to invade DRVN successfully, though keeping it and pacifying the populace is another question. The RVN is still in shamble around this time, further decreasing the success of the operation. Combination with the tactics of PAVN, the US would have to face a long drawn-out war over the entire Vietnam - and it would be more brutal than the OTL.
And all of this happened on the assumption the PRC and USSR wouldn't intervene. Just one of them provide intervention, things would go even more haywire