If you were a Spanish immigrant to Cuba, it would depend on what stock you came from. Are you coming as part of the Spanish military or bureaucracy? In that case you are likely to come, get wealthy from bribes, and leave shortly thereafter to enjoy your wealth back home. You likely accept slavery as necessary, and certainly beneficial for Spain, but have in the back of your mind that these so called pieces of property are still human. For example, you may make the scandalous step of calling black children niños (children) instead of negritos (little blacks) or cachorros (pups), which earned at least one Captain General of the 1830s a major backlash from plantation owning criollos.

If you're an immigrant, it is more likely you're from Galicia or some other impoverished part of Spain. In that case, you're likely to become a bodeguero (grocer). This guarantees you a middle class income and perhaps a slave or two to help you run the store. They're domestic slaves, though, so you treat them far better than field hands. You may not have the capital or the right mentality to be a grocer. In that case, you'll try to join up as a minor official, helping to administer the colony. After 1837, when a liberal constitution codifies Cuba's colonial status, you will enjoy extra privileges for not being a native criollo. Whatever you do within the world of the colonial administration, however, you will likely need a well connected figure in the administration looking out for you, obviously with the idea that you watch his back during the Byzantine power struggles within the administration or if Madrid starts looking into issues of corruption. You hope to return home with a nice bit of money saved up for you to retire, but if not you'll likely at least end up as a middle class owner of a middling store. You may not like slavery personally, you may be fine with it, it may horrify you because you didn't grow up around it (though you accept it as just a fact of life); it depends on a lot of factors. You certainly won't be calling for its abolition too loudly; that would be subversive.

This is, of course, if you aren't already coming from money. If you are a merchant you'll likely move to Cuba after one of the numerous planters who you've been loaning money to, at steep interest rates, goes bankrupt and you decide to run his plantation yourself. In this case, you'll likely end up marrying a wealthy white criollo woman yourself, perhaps one who has a noble title or two (purchased within the last hundred years, no doubt, from an indulgent Bourbon monarchy keen on ways to make money). Your children will likely turn out to be proudly criollo themselves and because of the plantation (and thus slave based) origins of your wealth, they will likely support Spain if push comes to shove, just to save their inheritance from social revolution or Spanish seizures. You see slaves as expedient and perhaps based in pseudo-scientific 'biological' explanations for why the institution must survive; your children will see it as natural and at the very least necessary to maintain the lifestyle they have enjoyed their entire lives.

Sources:

Ramon Meza: Mi Tio el Empleado (1887) (novel, but written by a contemporary about Spanish bureaucrats)

Cirilio Villaverde: Cecilia Valdes (1882) (also a novel, but specifically set by a contemporary in the period you mentioned)

Manuel Moreno Fraginals: El Ingenio (second edition, 1976) and Cuba/España España/Cuba (c. 2004)