Since it is an anomaly there won't be a trend
Depending on how literal you are about this statement, this might say it all.
The literal meaning of this is that nothing in your data is predictive of these anomalies. If that is the case, then the problem is, in some sense, impossible to solve. The conditional probability of an anomaly, conditioned on all present information (the entire history of the time series), says that an anomaly is unlikely and no more likely than at any other time with any other time series history. Nothing distinguishes the anomalies from the "business-as-usual" non-anomalies. In this case where the problem seems hopeless, if you want to make good forecasts of anomalies, you will have to bring in additional information, perhaps another time series that, alone or along with the current time series, is predictive of anomalies of interest. In the link, that additional information is when Easter occurs.
A less pessimistic read of the claim is that the trends might not be obvious but, you hope, are there for a sophisticated machine learning model to find. In that case, even if you cannot look at the time series and say, credibly and reliably, "An anomaly is likely to occur in 20-30 seconds," a good model might be able to pick up on trends that elude manual inspection.
In that case, you do have some information to credibly and reliably predict anomalies. While the marginal or overall probability of an anomaly might be very low (anomalies are uncommon, after all), the conditional probability of an anomaly is higher than usual. However, because of how unusual anomalies are, this probability might still be rather low, perhaps only $0.3$ instead of a baseline (overall) probability of $0.00003$.
This seems to be where you would want to use oversampling in order to boost the probability of an anomaly occurring in order to get a value above $0.5$, probably because a software package will then predict this as an anomaly when you run some kind of predict method. Scikit-learn works this way, for instance. The trouble with this approach, however, is that this is also likely to boost the predicted anomaly probability for non-anomaly events. You might get much better sensitivity to anomalies but at the expense of specificity and (probably) positive predictive value ("precision" in some circles).
What's another way to boost the sensitivity at the expense of the specificity? Look at the ROC curve and pick the threshold corresponding to a different point, and then use that threshold to bin the predicted probabilities into categories. In fact, changing the prior probability does not change the ROC curve, since ROC curves only depend on ranks and changing the prior corresponds to a rank-preserving transformation.
However, you don't even have to use thresholds at all. You can just predict the probability of an anomaly. Then oversampling, undersampling, or otherwise balancing the categories distorts the predicted probabilities, and there is little point in doing so outside of some special cases that are very-much outside the usual workflow of machine learning.
The utility of predicting probabilities instead of predicting classes is discussed on the blog of Frank Harrell, founding Chair of Biostatistics at Vanderbilt University.
Classification vs. Prediction
Damage Caused by Classification Accuracy and Other Discontinuous Improper Accuracy Scoring Rules
That many so-called "classification" models like logistic regressions and neural networks explicitly predict probability$^{\dagger}$ values and that these probabilities can be evaluated without any reference to a threshold is missed by many practioners of machine learning. Readers of those two Harrell blog articles will see that he finds this frustrating (as do I).
$^{\dagger}$These probabilities might not correspond to the real event probability, the subject of calibration. However, calibrated or not, they are legitimate Bernoulli probability parameters that satisfy the Kolmogorov axioms of probability. Whether or not they are good (calibrated) estimates of the conditional Bernoulli probability parameter is separate.
