I'd say no as well unless you are not planning on putting them in all at once.
It would be better to trellis tomatoes, cucumbers, and some kinds of squash. Trellising takes up less horizontal space. The trellis needs to be installed on the North end of your bed and make it 7 ft tall if you can. tomatoes and cucumber vines can get that tall.
4 trellissed cucumber vines will take up less space than 1 bush cucumber.
Garlic,carrots and bulbing onions depend on where you live. Please update your profile with your zone and location. I can only grow those things in Hawaii in the fall. Carrots and broccoli don't like temps greater than 70 very much. Green onions I can grow year round but I keep them in pots since they tolerate pots and they last more than a year.
If vines are not trellissed you need to give them space to wander. 1 squash vine can eat up all of your garden space and still will not be contained unless you let it sprawl outside. I once had a Tahitian sqash that ate up half my back lawn then went through the fence and tried to take over the neighbor's back yard. That was just one vine.
How is your bed configured? Is it a square or a rectangle? I am guessing it is about 4 ft wide and 20 ft long.
6 tomatoes will take up about half the garden unless you do two rows then it would take up 5 ft x 4 It would need to be on the North end not to shade plants behind it. (20 sq.ft)
A pepper can take about a sqare foot, but that is very close and peppers will have disease and pest issues with that kind of spacing. I would spread them out and plant other things between them like green onions and garlic if you can grow them now. Carrots IDK. Peppers and tomatoes like it warm 70-80 degree range, carrots like it cooler. I would be a better succession plant for cooler times. Beets will grow year round so that is a possibility and carrots, lettuce and beets will go together in cooler weather along with onions.
Broccoli is a large plant you will only get 2 plants accross and even if you offset plant so they will take up a lot of space unless you cut their leaves. (10-20 sqft) This is also a cool weather plant to plant with the carrots, lettuce, beets, greens,onions and garlic. It also does not like temps much higher than the mid 70's even the heat tolerant ones don't do well unless you are in the higher elevations and temps are less than 80.
Bush beans take up about 1 square foot they still may need staking. They produce all of their beans at once if you want to can them. Otherwise you will get a longer harvest and can plant more beans in a smaller space if you trellis them instead.
Summer squash like zucchini take up as much space as a bush cucumber which is 30-36 inch circle. Even if you let half of it hang out over the edge of the garden, vine zucchini and cucumbers take up less space on a trellis. 3 bush squash or cucumbers will take up 36 sq ft of the garden, but you can plant some small things around the squash, like beets, or radishes. Lettuce, spinach or bok choy can be planted in the cool months when the larger plants like tomatoes and peppers are still small and are not taking up all of the space yet. The lettuce will be harvested before the tomatoes and peppers need the space. One or two Swiss chard can be tucked in wherever there is space and it has repeat harvests. Swiss chard is one of the more heat tolerant greens.
I take it you are from the south since you are planting okra? Please update your profile with your location. Okra grows tall so it can be spread out with smaller plants between them. Some plants just do well together like tomatoes and basil, while others like fennel and just about everything else need to be separated.
You want to maximize the space in the garden, but it is sometimes better not to plant everything in the same place but to spread them out so they get better air circulation and you don't set up the buffet for the bugs. Also, this is something I have yet to master myself, be careful that you don't plant more than you can use of any one thing. If you plant multiple perishable things like lettuce, spinach, or greens, make sure you succession plant so you will have a continuous supply and everything lettuce or lettuce and bok choy do not have to be harvested at the same time or you may not be able to finish it off fast enough.
Most of your plants are big plants: tomatoes, peppers, broccoli, okra, squash and vines. These things take up a lot of space. Plant seasonal things around the big plants while they are small and are not using all of the space yet so it does not go to waste.
Trellis to save space or let things go out of the box like the vines.
Space your big plants and plant smaller things between them to make better use of the space and improve the air circulation
cool season: lettuce, small greens, bok choy, swiss chard, spinach, carrots, beets, radish, warm season: NZ spinach (this can take over) , Swiss chard, beets, black eyed peas, peanuts, and herbs between and under larger plants.
Since you have multiple boxes you can do family rotations. So you can do some companion planting in each box. Companion planting is not science based but based on observations made and passed on by real farmers over the years who learned the hard way what went well together and what does not. Separate enemies by at least 10 ft. I haven't had problems with them planted at that distance.
Try to plant things that I can get multiple harvest from like herbs, tomatoes, peppers, swiss chard, kale, collards, komatsuna, NZ hot weather spinach, chayote (fruits and shoots are edible), sweet potatoes (leaves are edible), taro ( two harvests a year leaves and tubers), ginger, green onions, eggplant, and edible gourds. Succession plant lettuce, Asian greens, spinach. Carrots I can only grow in cool weather with temps peaking around 70 degrees and they are cheap so not worth it unless there is nothing else to plant. I don't like beans but they do grow well if I get rust and nematode resistant Poamoho beans. Tomatoes, eggplant, peppers, and most herbs are in pots. They can be spread out as they grow. Tomatoes have to be trellissed and netted to keep the birds at bay. Kale and Swiss chard are good for repeat harvests. Planted in partial shade in summer and picked young they are less bitter, they get sweeter in cooler weather. Daikon and beets can be planted year round in the higher elevations in slightly more alkaline conditions. Asian greens are my winter rotation for summer corn. They scavenge nutrients left by the corn. I can grow heat tolerant greens under the ctrus trees in summer.
https://www.dal.ca/content/dam/dalhousi ... Online.pdf
https://www.peakprosperity.com/wsidblog ... p-rotation
http://www.almanac.com/content/companio ... vegetables
Happy gardening in Hawaii. Gardens are where people grow.