Let's start with what the books say:
The Dungeon Master's Workshop in the Dungeon Master's Guide has a section dedicated to calculated the challenge rating of custom monsters. There are two sections to analyze, Defensive Challenge Rating (DCR), and Offensive Challenge Rating (OCR).
With 28 HP and 10 AC, the DCR is 0. HP equals CR 1/8 while the lower AC brings it down to 0.
With a damage output of 3d4 (7) on a hit and 9d4 (22) on a failed save and a hit, we are looking at an OCR somewhere between of 1/2 and 3. The lower DC of 12, but higher to hit bonus of +4 balances out and we get an OCR of 1 or 2.
So your cube results in a CR of 1/2, already too high.
According to the same calculations, the standard gelatinous cube should only be a CR 1, so it is probable that Engulf and Ooze Cube is considered by the designers to be more powerful than the CR calculations account for.
As such, your Gelatinous Noob should calculate to CR 1/8 (and then be adjusted due to the power of Engulf and Ooze Cube to CR 1/4).
Why did you remove the weaknesses of gelatinous cubes?
Part of the balance of gelatinous cubes may also come from their low AC and low speed. I don't know why you removed these weaknesses in your smaller version, but they should still be present in some degree.
- Restore the original weaknesses (low AC and speed), although as a smaller creature perhaps its speed and AC are slightly higher (also matches the slightly higher Dexterity).
- Lower the damage output to reflect a CR 1/4, so that the overall CR becomes CR 1/8 (adjusted by the Engulf stuff to 1/4).
- Reduce the DC of Traits and Engulf to reflect DCs of the common CR 1/4 creature.
Here is the adjusted statblock:
Small ooze, unaligned
AC 8, HP 32 (5d8 + 10)
STR 14 DEX 7 CON 14 INT 1 WIS 6 CHA 1
Speed 20 ft
Condition Immunities Blinded, Charmed, Deafened, Exhaustion, Frightened, Prone
Senses Blindsight 60 ft., Passive Perception 8
Ooze Cube. The cube takes up its entire space. Other creatures can enter the space, but a creature that does so is subjected to the cube's Engulf and has disadvantage on the saving throw.
Creatures inside the cube can be seen but have total cover.
A creature within 5 feet of the cube can take an action to pull a creature or object out of the cube. Doing so requires a successful DC 11 Strength check, and the creature making the attempt takes 3 (1d6) acid damage.
The cube can hold only one Small creature or up to four Tiny creatures inside it at a time.
Transparent. Even when the cube is in plain sight, it takes a successful DC 13 Wisdom (Perception) check to spot a cube that has neither moved nor attacked. A creature that tries to enter the cube's space while unaware of the cube is surprised by the cube.
Pseudopod. +3 to hit, reach 5 ft., one creature, Hit: 3 (1d6) acid damage.
Engulf. The cube moves up to its speed. While doing so, it can enter Small or smaller creature's spaces. Whenever the cube enters a creature's space, the creature must make a DC 11 Dexterity saving throw.
On a successful save, the creature can choose to be pushed 5 feet back or to the side of the cube. A creature that chooses not to be pushed suffers the consequences of a failed saving throw.
On a failed save, the cube enters the creature's space, and the creature takes 3 (1d6) acid damage and is engulfed. The engulfed creature can't breathe, is restrained, and takes 10 (3d6) acid damage at the start of each of the cube's turns. When the cube moves, the engulfed creature moves with it.
An engulfed creature can try to escape by taking an action to make a DC 12 Strength check. On a success, the creature escapes and enters a space of its choice within 5 feet of the cube.
Part of why the Gelatinous Cube is such a threat (as I addressed earlier) is the Engulf and Ooze Cube traits. However, that is a threat because PCs are Medium or smaller in almost all cases, and are, as such, eligible to be engulfed (often many of them can be at once). It is highly possible that at a small size where most enemies are not eligible targets, the Ooze I propose does not satisfy CR 1/4 (since the pre-Engulf-adjustment CR is 1/8). In many ways it will require playtesting to verify balance as the Engulf action is very dynamic in its effectiveness.